I tested this build just for the fun of it after seeing the ap ratio of amumu, seeing how his q and r have a ratio of 1/1 and his e about .5/1 the damage output is rather impressive for a tank. its no morde but quite funny as hell.
pros:
- good damage burst
- slowing despair
cons:
- doesnt tank as much as tank build
thing you might want to remember is that most people will not focus the tank, and since most people see amumu as a tank they will most of the time not focuz you right away.

as you can see i start off my build with the basic gold per sec items to help me farm the gold required for the money, later on you wont need them and sell them off to complete your build.
the core items for this build are:

- sunfire cape
- abyssal scepter
- rylai's crystal scepter

with those item your despair becomes quite a weapon, enemies being around you will take good damage just by the sinergies that those 3 items gives to each other while still giving you some decent tanking power and hp.

its a fun build to try if you want to have fun, i know i did, your not as tanky as pure tank amumu but the damage outburst you have is amazing in teamfights.

to give you more or less the numbers ( give or take, saying this out of memory)
- q with an ap ratio of 1/1 did bout 800 dmg, stunned, slowed because of rylei and placed me in ranged for all my other skills.
- w despair did 24 dmg per second + 5.7% of their max hp, whitout counting the 35 dmg per second of sunfire and the -20 mr of abyssal scepter.
- e did about 600 and surrounded by minions or in teamfight its spammable
- r your ult that beautiful aoe did about 800-900 dmg and freezes enemies in their tracks for 2.5 sec, simply a killer move in teamfights with such dmg.