A338697 a(n) = [x^n] Product_{k>=1} 1 / (1 - n^(k-1)*x^k).

1, 1, 3, 13, 101, 931, 12391, 178809, 3331721, 66288142, 1589753211, 40104031166, 1183380156013, 36187564837217, 1262524447510383, 45533370885563716, 1834219414937219601, 76016894083755947753, 3479900167920331954531, 162982921698852088968886, 8341707623665223127224821

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..385

Formula

a(n) = Sum_{k=0..n} p(n,k) * n^(n-k), where p(n,k) is the number of partitions of n into k parts.

a(n) ~ c * n^(n-1), where c = BesselI(1,2) = A096789 = 1.590636854637329... - Vaclav Kotesovec, May 09 2021

Mathematica

Table[SeriesCoefficient[Product[1/(1 - n^(k - 1) x^k), {k, 1, n}], {x, 0, n}], {n, 0, 20}]
Join[{1}, Table[Sum[Length[IntegerPartitions[n, {k}]] n^(n - k), {k, 0, n}], {n, 1, 20}]]
Join[{1}, Table[SeriesCoefficient[x + (n-1)/(n*QPochhammer[1/n, n*x]), {x, 0, n}], {n, 1, 20}]] (* Vaclav Kotesovec, May 09 2021 *)

Crossrefs

Cf. A008284, A075900, A124577, A300579, A338673, A338674, A338675, A338676, A338677, A338678, A338679, A344095.

Sequence in context: A267196 A268215 A323687 * A168417 A352170 A240167

Adjacent sequences: A338694 A338695 A338696 * A338698 A338699 A338700

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 24 2021

Status

approved