A384044 a(n) = [x^n] Product_{k=1..n} (1 + k^3*x) / (1 - k^3*x).

1, 2, 162, 75672, 104312000, 317309605650, 1803288012589602, 17180843554017736544, 254292459616733559570432, 5525508321588276184345621650, 168733575675064578625834983478850, 6994229599670887851052241626545021912, 382562895157136117988572795915676719695680

Offset: 0

Author

Vaclav Kotesovec, May 18 2025

Keywords

• nonn

Crossrefs

Cf. A000442, A351800.

Cf. A350366, A384043, A351764.

Programs

Mathematica

Table[SeriesCoefficient[Product[(1+k^3*x)/(1-k^3*x), {k, 1, n}], {x, 0, n}], {n, 0, 12}]

Formula

a(n) ~ c * d^n * n!^3 / n^2, where d = 37.604795475701444958019770120055586495991039059348094619704... and c = 0.063895861310548119570865800164582089372152350471371583403...