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, -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

Table of n, a(n) for n=0..22.

N. J. A. Sloane, Transforms

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

Cf. A001008, A002805, A028343, A303970, A304494.

Sequence in context: A089750 A109591 A143932 * A195258 A370450 A070471

Adjacent sequences: A304493 A304494 A304495 * A304497 A304498 A304499

Keyword

sign

Author

Ilya Gutkovskiy, May 13 2018

Status

approved