A320844 Expansion of Product_{k>0} (1-x^p(k)), where p(k) is the number of partitions of k (A000041).

1, -1, -1, 0, 1, 0, 0, 0, 1, 0, -1, -1, 1, 1, -1, -2, 2, 2, -1, -2, 0, 1, -1, 0, 1, 2, 0, -2, -2, 2, -1, 0, 1, 2, -1, -1, 0, 2, -3, -2, 1, 3, -1, 0, 1, 3, -3, -4, 0, 4, 1, -3, 1, 2, -1, -4, -1, 5, 2, -4, 0, 3, 1, -3, -1, 0, 1, -3, 1, 3, 3, -2, -2, -2, 1, -1, 1, 1, 3, -3

Offset: 0

Author

Seiichi Manyama, Oct 22 2018

Keywords

• sign
• look

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000

Crossrefs

Convolution inverse of A007279.

Cf. A000041, A280253.

Programs

Magma

m:=50; R:=PowerSeriesRing(Integers(), m); Coefficients(R!( (&*[1-x^NumberOfPartitions(k): k in [1..100]]))); // G. C. Greubel, Oct 27 2018

Mathematica

CoefficientList[Series[Product[1 - x^PartitionsP[k], {k, 1, 120}], {x, 0, 100}], x] (* G. C. Greubel, Oct 27 2018 *)

PARI

x='x+O('x^50); Vec(prod(k=1,50, 1-x^numbpart(k))) \\ G. C. Greubel, Oct 27 2018