cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A255268 #11 Feb 16 2025 08:33:25
%S A255268 1,4,1728,6879707136,49302469038676377600000,
%T A255268 237376313799769806328950291431424000000000000,
%U A255268 487929826521303413461947888047619993419888153407795494912000000000000000000000
%N A255268 a(n) = Product_{k=1..n} k!^n.
%H A255268 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BarnesG-Function.html">Barnes G-Function</a>
%H A255268 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Superfactorial.html">Superfactorial</a>
%F A255268 a(n) = A000178(n)^n.
%F A255268 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).
%t A255268 Table[Product[k!,{k,1,n}]^n,{n,1,10}]
%t A255268 Table[BarnesG[n+2]^n, {n, 1, 10}]
%Y A255268 Cf. A000178, A055462, A074962, A255269.
%K A255268 nonn
%O A255268 1,2
%A A255268 _Vaclav Kotesovec_, Feb 20 2015