An alternative route is the pure AP burst route. 9/0/21 forgoing the biscuit.

Open sapphire crystal + pots
Upgrade crystal -> Tear
Boots
Sheen -> Lichbane
Needlessly Large Rod -> Deathfire Grasp (this is part of your burst combo and gives CDR for Q)
Needlessly Large Rod -> Rabadon's Deathcap (this powers the burst combo)
Complete Seraph's Embrace
If the game goes really long, Zhonya's Hourglass for survivability

This is a squishy combo mage version. It uses lifesteal bursts to stay alive as your Q will hit stupidly hard with Lichbane. You time your ultimate after you take some initial damage so it gives you the 600 health back so you are a little less squishy. Seraph's Embrace shield can be put up for additional survivability lategame along with an hourglass proc if it goes super long.

Can't say I recommend it but it's a blast to see how much damage you can do with it. Just keep in mind that Lichbane has a cooldown so timing abilities to maximize your Lichbane procs helps.

Just tried rushing IBG in a bot game. I murdered the bots, but that's not really much of a surprise. Here are some notes I found.
1) Damage is fairly low though mid game. Until I actually build my NLR my damage was pretty abyssmal. In fact IBG doesn't give much damage becasue the build is so AP heavy. It my be ideal to rush NLR before IBG just to make the build last in the mid game.

2) Survivabilty is pretty good. Granted my mastery page has the regen per mana mastery and I actually use Spell vamp quints because I don't have enough flat AP quints which helps alot with helth regen. IBG provides some good protection from AD and merc treads from AP. You are pretty tanky early.

3) Liandry's does provide some great damage, and with Deathcap you just pass 300 AP to hit the cap.

4) Q farming is difficult. I tested both tiamat and IBG. Neither on-hit splah will provide bonus farm to your Q. If you hit Q and kill minions with the splash damage it doesn't count as feed for your Q's bonus damage. It does help you push like a monster though.

5) It is nice to build some AD after IBG though, it makes a large difference in the damage. However, I am unsure about Hydra. Maybe it would be better just to go straight BT. The extra lifesteal would add alot to sustain and damagefor the IBG. I think that's the way I'd go. After that, I'm not really sure. Probably some sustain in the form of Warmog's I guess.

6) One final note, I've been putting five points in offense masteries to get the 5% extra damage to turrets. Nasus already pushes turrets excellently, and I find this makes him melt them even faster.

Nashor's Tooth - It gives nice CDR, AP, and attack speed. It's a great item for Nasus. I just wish they hadn't removed the mana regen from it.

Trinity Force - It's expensive, the slow requires attack speed to be effective, and it needs AD for it's Sheen effect. It also has every stat Nasus needs as a hybrid and seeing pros using this in their streams while using Nasus top has made me reexamine how good it is for him.

The Black Cleaver - CDR, AD, Health, and Armor Shred that also helps the team. The Brutalizer is a nice early build piece granting some damage and some CDR.

Zhonya's Hourglass - High AP, Armor, save posterior special.

Rod of Ages - Health, Mana, AP.

Mercury Treads - MR, Movespeed, Tenacity, Homeguard

These have potential to me. It would just max out the 300 AP you need, max out CDR, plenty of attack speed, move speed, high health, some armor and MR, mana for sustain, a Sheen effect, a Slow effect, armor shred, even a little critical chance in case you feel lucky. Hourglass on use.

But what order do you put them in and would it be better to build some of the base items early: Seeker's Armguard is great for the price. So is Brutalizer. Stinger isn't bad either. Catalyst would be needed early to slow OOM. You obviously need Boots early. Getting Nashor's Tooth early means faster Q farming but will mana be an issue with faster Qs. That's the part that is troubling me. If you do it wrong, your early game suffers and you don't get a late game. Delay CDR too long and you will stunt the growth of your Q farm.

Thus more testing. My current test is running items in this order: Rod of Ages, Boots when necessary, Trinity Force, Nashor's Tooth, Zhonya's Hourglass, The Black Cleaver. Also switching runes to Hybrid Penetration instead of magical shows an increase in DPS. Which makes sense in a hybrid build. You won't be a major tank but you won't be squishy either. I would love to lead with Nashor's Tooth but mana becomes an issue. If Rod wasn't necessary, I'd prefer Liandry's Torment. A little squishier but the damage would be great on the AoEs.

Thus more testing. Ideas welcome.

Figured it out. The key was not to upgrade E as quickly so that mana cost didn't escalate as high. Then starting Sheen gives you enough mana to make it workable. So this is the path:

Opened Doran's Ring + Pot + Biscuit
1) Sapphire Crystal + Boots + Ward
2) Sheen + Ward
3) Haunting Guise + Ward
4) Mercury Treads + Ward Upgrade to boot enchant of choice when ready.
5) Liandry's Torment
6) Phage + Pink Ward
7) Trinity Force
8) Giant's Belt + Pink Ward
9) Rylai's Crystal Scepter

This setup makes it more difficult to kite you. You have a ranged slow (15%), Trinity slow, and Wither. The move speed bonus of Trinity is better than the Phantom Dancer that the ADC will have. At 1050 bonus health, you are tanky enough and with Liandry's, you do a lot of AoE damage. You'll need to Q farm more and E farm less as the game progresses to make the mana work.

10) Nashor's Tooth - You attack faster which makes proccing Trinity slow more precise. You get AP to power your spells. You get CDR to farm your Qs faster.

Chances are the game ended by this point or sooner but sometimes games get stalemated. At this point, you are close to the AP cap (275ish). So time for your first melee oriented item.

11) The Black Cleaver. More health, more CDR, armor shred, and AD. Everything a growing dog needs.

12) Sell Doran's Ring for Guinsoo's Rageblade. This will cap your AP, gives you more healing when you need it and even more attack speed to max out the AD bonus from your ultimate.

This path feels much better to me. Testing is continuing. But this feels right. At endgame, you have capped CDR, capped ultimate, health burning AoEs with slows, a lot of attack speed to go with the AD bonus from ultimate, a ton of health, a mighty Q, and innate lifesteal to keep you alive. Your attacks in Spirit Fire shred 25% of their armor + another 50 so a 200 armor tank drops to 100 armor.

All in all, I feel a lot happier with this path. If this success continues, I'll change the OP.

Testing continuing. I don't have any high-level testers yet (Diamond 3 or better) so you're warned. Seeing an occasional bug where Liandry's is refreshing but it's doing no damage. The mana is doing better than I expected alternating Q/E and it may be possible that opening a non-mana item would be ok if proper mana management is used. Still feel opening Sheen into Boots/Liandry's is the best start.

I would like to see some high-level testers, but I like the look of this build. I think the skill leveling for mana management is a good idea, and building moer ap after sheen definitely helps keep Nasus' power level up through mid game. I think this build would be viable in top lane as well as mid since it is essentially hybrid bruiser lane.

Just my 2c but its seems like going the triforce route, you re-introuduce a lot of the issues that knocked the traditional AD Nausus build out of viability in the first place. Keep in mind the Trieforce only scales on your BASE AD, so there is no synergy with your other items or with your Q. The slow really isn't needed, especially if you are already building ryalias. Just not seeing what the new build brings that makes it worth sacrificing the strong early/mid game that you get from Lichbane.

@vortical42: That's the hybrid build that I'm working on. The duo slows actually work well together. Here's how it works:

You want to tunnel an ADC but you know he's got cleanse. You open with wither and try to close the gap. He cleanses the wither. You hit with Spirit Fire which gives that ADC a 15% slow and hit ghost which combines with your move speed to close the gap. Once you close the gap, your Triforce procs keep the ADC slowed. But I bet you're wondering why you need Triforce procs to keep him slowed.

The thing about Rylai's is that it only lasts 1.5 sec. But Q's cooldown is bigger than that even with max CDR. So having additional slows increases the chance that you keep that ADC locked down long enough for the kill. The more attack speed you have, the higher the chance Triforce gives you the slow you need.

The opposing team will try to peel you from the ADC. Your team will be using their CC to try to give you a clear path to the ADC (peeling the peelers). If you reach the ADC for more than a couple seconds, he's dead and he knows it. The team that executes it better will have the best results.

End result: you are much harder to kite than your standard Nasus because you have the ranged slow to go with your close range slow as well as Ghost/Flash to keep you in their face. You have higher movement speed than any ADC with Statikk Shiv/Phantom Dancer due to the 8% movespeed bonus from trinity and the 3% bonus from Nimble. So unless you're dealing with Ezreal with Frozen Fist, you should reach them. If you are facing Ezreal, your team needs to blow a CC on Ezreal to force a cleanse so your wither can land cleanly. After that, he can't kite you at all.

Level 14 comparison for Lichbane vs Trinity Force. Both bought boots. AP gets Rod. Hybrid gets Liandry's.
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In the main build, Lichbane hits for 50 + (0.75 x 150) assuming rod is half complete = 162.5 dmg.
In the hybrid build, Trinity hits for (assuming level 14) 102 * 1.5 = 153 dmg.

So when you reach the second major item threshold, their damage is almost the same. But Trinity also gives 30AD and 30% attack speed to your melee attacks which more than makes up the difference between the two items. Which makes sense. Hybrid does more damage in melee range.

Lichbane gets more powerful as you build more AP items. Trinity's AD and attack speed get more powerful when you build the hybrid items. They both act as force multipliers. They make your other items scale better in terms of total DPS.

The primary AP build on the OP is a tanky build that so happens to put out a good amount of damage at range. Your role in team fights will be to land that AoE damage and move in to absorb a good amount of the damage your opposing team dishes out. If you can land a Q, it'll hurt a lot but it's the threat of your Q that makes it work. The opposing team is forced to blow peels, damage, and CC on you when you're essentially a tank with a ton of HP and armor with a potential hourglass. If they are spending that peel on you (who already did a lot of AoE dmg + armor shred), who on your team isn't getting peeled and how much damage are they doing as a result?

The hybrid route is less tanky with more sustained damage but you're still way tankier than your average mid while doing quite a lot of AoE damage. Doran's/Liandries/Trinity/Rylai's is 1130 health. That isn't chump change by any standard. Going hybrid rewards you more if you can reach your target but offers less ranged damage and tankiness as a drawback.

Which should you choose?
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Does your team have the CC available to get you to your target? If yes, you can go hybrid because you'll do more damage up close.

Does your team desperately need a tank? If yes, you should use the AP build with added tank items instead of Liandry's/Rylai's. You'll be very tanky with some AoE damage as a bonus.

Does your team lack a lot of CC but have a tank? Standard OP build. You'll probably be the second tankiest or tankiest guy on your team even with your AoE damage build. The raw AoE damage you put out will be quite substantial considering how incredibly tanky you'll be.

Bump!

Interesting. Thanks for taking the time to explain that, it makes a lot more sense now.