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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 (list; graph; refs; listen; history; text; internal format)
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 A070471 A070690

Adjacent sequences:  A304493 A304494 A304495 * A304497 A304498 A304499

KEYWORD

sign

AUTHOR

Ilya Gutkovskiy, May 13 2018

STATUS

approved

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Last modified January 27 16:30 EST 2022. Contains 350608 sequences. (Running on oeis4.)