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A304784 Expansion of Product_{k>=1} 1/(1 + x^k)^p(k), where p(k) = number of partitions of k (A000041). 1
1, -1, -1, -2, 0, -1, 2, 3, 11, 8, 19, 13, 22, -5, -10, -80, -105, -246, -303, -502, -506, -681, -400, -231, 873, 1956, 4733, 7536, 12891, 17609, 25188, 29508, 34890, 29690, 19039, -17742, -74002, -183563, -333665, -572271, -866683, -1271429, -1698491, -2181207 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Convolution inverse of A261049.

LINKS

Table of n, a(n) for n=0..43.

Eric Weisstein's World of Mathematics, Partition Function P

Index entries for sequences related to partitions

FORMULA

G.f.: Product_{k>=1} 1/(1 + x^k)^A000041(k).

MATHEMATICA

nmax = 43; CoefficientList[Series[Product[1/(1 + x^k)^PartitionsP[k], {k, 1, nmax}], {x, 0, nmax}], x]

a[n_] := a[n] = If[n == 0, 1, Sum[Sum[(-1)^(k/d) d PartitionsP[d], {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 43}]

CROSSREFS

Cf. A000041, A001970, A089254, A261049, A300508.

Sequence in context: A115218 A023858 A011118 * A131644 A115346 A140531

Adjacent sequences:  A304781 A304782 A304783 * A304785 A304786 A304787

KEYWORD

sign

AUTHOR

Ilya Gutkovskiy, May 18 2018

STATUS

approved

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Last modified June 16 21:18 EDT 2019. Contains 324155 sequences. (Running on oeis4.)