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 A366329 #18 Apr 19 2024 03:11:56
%S A366329 1,5,324,589764,52393770000,347773153451938500,
%T A366329 244632735619259069507040000,24547871392966749661547369532868031040,
%U A366329 455140097017244017295446005144727669016636127744000,1960564895414510364772369567330640938816177001699555385515625000000
%N A366329 a(n) = Product_{k=1..n} Sum_{j=1..k} j^n.
%F A366329 a(n) = A036740(n) * Product_{k=1..n} Sum_{j=1..k} (j/k)^n.
%F A366329 a(n) ~ n!^n * c * d^n, where d = exp(-Integral_{x=0..1} log(1 - exp(-1/x)) dx) = 1.187538543919977798892363400109897833660222697152558038684860736484... and c = exp(1 - 1/(exp(1) - 1)) / (exp(1) - 1) = 0.88399704290317414073109479991305699114875723090346..., updated Apr 19 2024
%F A366329 a(n) ~ c * d^n * (2*Pi)^(n/2) * n^(n*(2*n+1)/2) / exp(n^2 - 1/12).
%t A366329 Table[Product[Sum[j^n, {j, 1, k}], {k, 1, n}], {n, 1, 12}]
%t A366329 Table[Product[HarmonicNumber[k, -n], {k, 1, n}], {n, 1, 12}] // FunctionExpand
%Y A366329 Cf. A031971, A036740, A366305, A366342.
%K A366329 nonn
%O A366329 1,2
%A A366329 _Vaclav Kotesovec_, Oct 07 2023