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 A372117 #7 Apr 19 2024 17:38:01
%S A372117 1,2,108,3200000,1158107343750000,119025168578031262646195453952,
%T A372117 82864944710388642300699757862681018776776867840000,
%U A372117 9481019710293786574190900386319772308050021208649248212215823364196925440000000
%N A372117 a(n) = Product_{k=0..n} binomial(n+k, k)^k.
%F A372117 a(n) = Product_{k=0..n} binomial(n + k, n)^k.
%F A372117 a(n) = A372116(n) / (A255269(n) * A067055(n)).
%F A372117 a(n) ~ 2^(2*n^3/3 + 3*n^2/4 + n/6 + 1/24) * exp(n^3/12 + n^2/4 - n/24 + zeta(3)/(8*Pi^2) - 1/24) / (sqrt(A) * Pi^(n^2/4 + n/4) * n^(n^2/4 + n/4 + 1/24)), where A is the Glaisher-Kinkelin constant A074962.
%t A372117 Table[Product[Binomial[n+k,k]^k, {k,0,n}], {n,0,10}]
%Y A372117 Cf. A067055, A255269, A306789, A362288, A372116.
%K A372117 nonn
%O A372117 0,2
%A A372117 _Vaclav Kotesovec_, Apr 19 2024