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%I #7 Sep 08 2018 05:22:47
%S 1,1,3,20,103,899,8143,84678,975049,13082993,186340631,2878977408,
%T 48899305783,876721463435,16971889682707,349059348881834,
%U 7565120836998801,173313418321443809,4197655086606145387,106097089652021765356,2816940203630838490791,78147038018470085005235
%N Expansion of e.g.f. Product_{k>=1} (1 + x^k)^H(k), where H(k) is the k-th harmonic number.
%H Vaclav Kotesovec, <a href="/A304494/b304494.txt">Table of n, a(n) for n = 0..438</a>
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F E.g.f.: Product_{k>=1} (1 + x^k)^(A001008(k)/A002805(k)).
%t nmax = 21; CoefficientList[Series[Product[(1 + x^k)^HarmonicNumber[k], {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
%t 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}]
%Y Cf. A001008, A002805, A168243, A303970, A304496.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, May 13 2018
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