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A304494 Expansion of e.g.f. Product_{k>=1} (1 + x^k)^H(k), where H(k) is the k-th harmonic number. 3
1, 1, 3, 20, 103, 899, 8143, 84678, 975049, 13082993, 186340631, 2878977408, 48899305783, 876721463435, 16971889682707, 349059348881834, 7565120836998801, 173313418321443809, 4197655086606145387, 106097089652021765356, 2816940203630838490791, 78147038018470085005235 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 27 06:18 EST 2022. Contains 350601 sequences. (Running on oeis4.)