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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
OFFSET
0,3
LINKS
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
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, May 13 2018
STATUS
approved