Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #6 Apr 21 2024 11:40:19
%S 1,1,16,161243136,1953714516870533385423459188736,
%T 18637697331204402735774894643901575833450808531469488619520000000000000000000000000
%N a(n) = Product_{k=1..n} k!^(k^2).
%F a(n) ~ (2*Pi)^(n^3/6 + n^2/4 + n/12) * n^(n^4/4 + 2*n^3/3 + n^2/2 + n/12 - 1/90) / (A^(1/6) * exp(5*n^4/16 + 5*n^3/9 + n^2/8 - n/12 - zeta(3)/(8*Pi^2) - zeta'(-3)/3 - 13/720)), where A is the Glaisher-Kinkelin constant A074962, zeta(3) = A002117, zeta'(-3) = A259068.
%t Table[Product[k!^(k^2), {k, 1, n}], {n, 0, 6}]
%Y Cf. A051675, A255269.
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, Apr 20 2024