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 A366342 #13 Apr 01 2024 10:00:01 %S A366342 1,5,180,63720,281961000,18939602331000,22733280436308624000, %T A366342 561162207057469095693888000,322278252906706683140441912431680000, %U A366342 4806568058842248598039183477606983722184000000,2055653754202086984879290521714456895014175320595424000000 %N A366342 a(n) = Product_{k=1..n} Sum_{j=1..k} j^k. %F A366342 a(n) = A002109(n) * Product_{k=1..n} Sum_{j=1..k} (j/k)^k. %F A366342 a(n) ~ A002109(n) * c * d^n / n^f, where %F A366342 d = 1/(1 - exp(-1)) = A185393 %F A366342 f = (exp(1) + 1) / (2*(exp(1) - 1)^2) = 0.629685240773129106752912520161993823... %F A366342 c = 1.038111196610478473178942324022485064169644880240145128332184584611... %F A366342 a(n) ~ A * c * d^n * n^(n*(n+1)/2 + 1/12 - f) / exp(n^2/4), where A is the Glaisher-Kinkelin constant A074962. %t A366342 Table[Product[Sum[j^k, {j, 1, k}], {k, 1, n}], {n, 1, 12}] %t A366342 Table[Product[HarmonicNumber[k, -k], {k, 1, n}], {n, 1, 12}] // FunctionExpand %Y A366342 Cf. A002109, A031971, A074962, A185393, A366329. %K A366342 nonn %O A366342 1,2 %A A366342 _Vaclav Kotesovec_, Oct 07 2023