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A304496
Expansion of e.g.f. Product_{k>=1} (1 - x^k)^H(k), where H(k) is the k-th harmonic number.
1
1, -1, -3, -2, 3, 261, 745, 12412, 16289, -260081, -5424199, -96985734, -2047127621, -17402659299, -84365982987, -2937186832544, 39650368238977, 1047895936025183, 35975009604881845, 638531451763185398, 14668256344792565331, 248159858571597211093, 6320237684944085611809
OFFSET
0,3
LINKS
FORMULA
E.g.f.: Product_{k>=1} (1 - x^k)^(A001008(k)/A002805(k)).
MATHEMATICA
nmax = 22; 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[d HarmonicNumber[d], {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[n! a[n], {n, 0, 22}]
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, May 13 2018
STATUS
approved