Another What's the next number?

[holomorphic]

Another "What's the next number?"

Someone posted one of these recently and I just felt like putting up some recklessly-devised next number question of my own. I like these!

So, what is it?

1, 9, 625, 117649, 531441, 25937424601, 23298085122481, 2562890625, ...?

 

[transphenomen]

Well, if it wasn't for the 5th and 8th one, I would say it was (2x+1)^2x for x=0,1,2,3...

 

[Dickfore]

Well, if it wasn't for the 5th and 8th one, I would say it was (2x+1)^2x for x=0,1,2,3...

this.

so, the guess would be:

x = 8 => 17¹⁶ = 48,661,191,875,666,868,481

 

[willem2]

this.

so, the guess would be:

x = 8 => 17¹⁶ = 48,661,191,875,666,868,481

and x = 9 => 19¹⁸ as well, but

for x = 10 you get 7355827511386641 =21¹²

 

[holomorphic]

Well, if it wasn't for the 5th and 8th one, I would say it was (2x+1)^2x for x=0,1,2,3...

Yeah, aside from the odd bases, there's just one more trick.