cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A304496 Expansion of e.g.f. Product_{k>=1} (1 - x^k)^H(k), where H(k) is the k-th harmonic number.

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%I A304496 #4 May 13 2018 20:49:28
%S A304496 1,-1,-3,-2,3,261,745,12412,16289,-260081,-5424199,-96985734,
%T A304496 -2047127621,-17402659299,-84365982987,-2937186832544,39650368238977,
%U A304496 1047895936025183,35975009604881845,638531451763185398,14668256344792565331,248159858571597211093,6320237684944085611809
%N A304496 Expansion of e.g.f. Product_{k>=1} (1 - x^k)^H(k), where H(k) is the k-th harmonic number.
%H A304496 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F A304496 E.g.f.: Product_{k>=1} (1 - x^k)^(A001008(k)/A002805(k)).
%t A304496 nmax = 22; CoefficientList[Series[Product[(1 - x^k)^HarmonicNumber[k], {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
%t A304496 a[n_] := a[n] = If[n == 0, 1, Sum[-Sum[d HarmonicNumber[d], {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[n! a[n], {n, 0, 22}]
%Y A304496 Cf. A001008, A002805, A028343, A303970, A304494.
%K A304496 sign
%O A304496 0,3
%A A304496 _Ilya Gutkovskiy_, May 13 2018