A304494 Expansion of e.g.f. Product_{k>=1} (1 + x^k)^H(k), where H(k) is the k-th harmonic number.

1, 1, 3, 20, 103, 899, 8143, 84678, 975049, 13082993, 186340631, 2878977408, 48899305783, 876721463435, 16971889682707, 349059348881834, 7565120836998801, 173313418321443809, 4197655086606145387, 106097089652021765356, 2816940203630838490791, 78147038018470085005235

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..438

N. J. A. Sloane, Transforms

Formula

E.g.f.: Product_{k>=1} (1 + x^k)^(A001008(k)/A002805(k)).

Mathematica

nmax = 21; CoefficientList[Series[Product[(1 + x^k)^HarmonicNumber[k], {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = If[n == 0, 1, Sum[Sum[(-1)^(k/d + 1) d HarmonicNumber[d], {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[n! a[n], {n, 0, 21}]

Crossrefs

Cf. A001008, A002805, A168243, A303970, A304496.

Sequence in context: A000948 A074831 A203357 * A000917 A025535 A119693

Adjacent sequences: A304491 A304492 A304493 * A304495 A304496 A304497

Keyword

nonn

Author

Ilya Gutkovskiy, May 13 2018

Status

approved