A366342 a(n) = Product_{k=1..n} Sum_{j=1..k} j^k.

1, 5, 180, 63720, 281961000, 18939602331000, 22733280436308624000, 561162207057469095693888000, 322278252906706683140441912431680000, 4806568058842248598039183477606983722184000000, 2055653754202086984879290521714456895014175320595424000000

Offset

1,2

Links

Table of n, a(n) for n=1..11.

Formula

a(n) = A002109(n) * Product_{k=1..n} Sum_{j=1..k} (j/k)^k.

a(n) ~ A002109(n) * c * d^n / n^f, where

d = 1/(1 - exp(-1)) = A185393

f = (exp(1) + 1) / (2*(exp(1) - 1)^2) = 0.629685240773129106752912520161993823...

c = 1.038111196610478473178942324022485064169644880240145128332184584611...

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.

Mathematica

Table[Product[Sum[j^k, {j, 1, k}], {k, 1, n}], {n, 1, 12}]
Table[Product[HarmonicNumber[k, -k], {k, 1, n}], {n, 1, 12}] // FunctionExpand

Crossrefs

Cf. A002109, A031971, A074962, A185393, A366329.

Sequence in context: A035791 A324090 A250327 * A162136 A053363 A027572

Adjacent sequences: A366339 A366340 A366341 * A366343 A366344 A366345

Keyword

nonn

Author

Vaclav Kotesovec, Oct 07 2023

Status

approved