A255268 a(n) = Product_{k=1..n} k!^n.

1, 4, 1728, 6879707136, 49302469038676377600000, 237376313799769806328950291431424000000000000, 487929826521303413461947888047619993419888153407795494912000000000000000000000

Offset: 1

Author

Vaclav Kotesovec, Feb 20 2015

Keywords

• nonn

Links

• Eric Weisstein's World of Mathematics, Barnes G-Function
• Eric Weisstein's World of Mathematics, Superfactorial

Crossrefs

Cf. A000178, A055462, A074962, A255269.

Programs

Mathematica

Table[Product[k!,{k,1,n}]^n,{n,1,10}]
Table[BarnesG[n+2]^n, {n, 1, 10}]

Formula

a(n) = A000178(n)^n.

a(n) ~ exp(1/12 + n/12 - n^2 - 3*n^3/4) * n^(5*n/12 + n^2 + n^3/2) * 2^(n/2 + n^2/2) * Pi^(n/2 + n^2/2) / A^n, where A = 1.28242712910062263687534256886979... is the Glaisher-Kinkelin constant (see A074962).