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.
%I A372116 #7 Apr 19 2024 17:38:06
%S A372116 1,2,3456,128994508800000,21048441369734473363614597120000000000,
%T A372116 13080442484467245346116306952031286205761554346416540536012800000000000000000000
%N A372116 a(n) = Product_{k=0..n} (n+k)!^k.
%C A372116 The next term has 146 digits.
%F A372116 a(n) ~ 2^(2*n^3/3 + 5*n^2/4 + 2*n/3 + 1/24) * Pi^(n*(n+1)/4) * n^(5*n^3/6 + 5*n^2/4 + 5*n/12) / exp(31*n^3/36 + 7*n^2/8 - 1/24).
%F A372116 For n>=1, a(n) = a(n-1) * A368132(n) * (2*n-1)!^n.
%t A372116 Table[Product[(n + k)!^k, {k, 0, n}], {n, 0, 8}]
%Y A372116 Cf. A055462, A255269, A296591, A367492, A368132.
%K A372116 nonn
%O A372116 0,2
%A A372116 _Vaclav Kotesovec_, Apr 19 2024