So, I did the math for the maximum ammount of AP Veigar can get...

I was kind of bored, so I decided to find out how much Ability Power a Veigar could (theoretically) get. (not counting Q stacks) The build is Deathcap, Seraph's Embrace and 4x Rod of Ages. You get Deathcap and Seraph's for their passives, (+35% AP and gives you AP equal to 3% of your max mana) and the Rods because their passive stacks. At max stacks, a Rod gives you 800 mana and 120 AP. (plus some health, but we don't care about that shit) You get 15 AP (this is essential) from Masteries at lv18, and you get all scaling runes, which gives you 83.16 AP at lv18. Veigar gets 1276 mana at lv18, plus the mana from the Rod(s) and Seraph's is 5476, which grants 164.28 AP from the Seraph's passive. The AP from the Rod(s), Deathcap and Seraph's is 680, plus the AP from the Seraph's passive, (164.28) runes, (83.16) and masteries (15) comes to a grand total of 942.44. That might not seem like much, but we haven't added the Deathcap passive yet. It grants +35% AP, which is 329.854. That comes to a grand[er] total of 1,272.294, assuming he doesn't last hit shit with Q. (Of course, it would take 40 minutes to stack out all of the Rods, not counting the time it takes to get the gold actually buy the items)

Edit: Deep Terror Nami (NA) brought up a good point about buffs, so with the Elixer of Sorcery, Hand of Baron, Dragon Slayer and Zeke's Harbinger, it brings your AP (temporarily) up to 1,772.905968

Edit 2: Since we're doing buffs, we might as well throw in blue buff. (gives +2 AP per level) So that's 942.44 AP from the Rods, Deathcap, Seraph's and Seraph's passive, plus 90 AP from the Elixer and Hand of Baron, (1,032.44) blue buff, (1,068.44) Deathcap passive, (1,442.394) Zeke's buff, (1,730.8728) and Dragon Slayer brings it up to a grand[est] total of 1,834.725168 Ability Power.