A284899 Expansion of Product_{k>=1} 1/(1+x^k)^(k^5) in powers of x.

1, -1, -31, -212, -284, 4935, 43719, 160002, -96747, -4914512, -31358932, -94515285, 97642670, 2823746182, 16834776254, 51617810512, -11233909783, -1137004349695, -7267899354808, -25263858110877, -24537905293857, 319397811973578, 2523465326904492

Offset: 0

Author

Seiichi Manyama, Apr 05 2017

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..2647

Crossrefs

Cf. A248884.

Product_{k>=1} 1/(1+x^k)^(k^m): A081362 (m=0), A255528 (m=1), A284896 (m=2), A284897 (m=3), A284898 (m=4), this sequence (m=5).

Programs

Mathematica

CoefficientList[Series[Product[1/(1 + x^k)^(k^5) , {k, 40}], {x, 0, 40}], x] (* Indranil Ghosh, Apr 05 2017 *)

PARI

x= 'x + O('x^40); Vec(prod(k=1, 40, 1/(1 + x^k)^(k^5))) \\ Indranil Ghosh, Apr 05 2017

Formula

a(0) = 1, a(n) = -(1/n)*Sum_{k=1..n} A284927(k)*a(n-k) for n > 0. - Seiichi Manyama, Apr 06 2017