A284897 Expansion of Product_{k>=1} 1/(1+x^k)^(k^3) in powers of x.

1, -1, -7, -20, -8, 99, 455, 958, 715, -3606, -17450, -44157, -61852, 19546, 419786, 1442212, 3084950, 3756436, -2155907, -27112107, -88277693, -187777531, -251308697, -5153980, 1182558343, 4299818445, 9988792754, 16075200671, 12020651310, -29802956283

Offset: 0

Author

Seiichi Manyama, Apr 05 2017

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..7180

Crossrefs

Cf. A248882.

Product_{k>=1} 1/(1+x^k)^(k^m): A081362 (m=0), A255528 (m=1), A284896 (m=2), this sequence (m=3), A284898 (m=4), A284899 (m=5).

Programs

Mathematica

CoefficientList[Series[Product[1/(1 + x^k)^(k^3) , {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^3))) \\ Indranil Ghosh, Apr 05 2017

Formula

a(0) = 1, a(n) = -(1/n)*Sum_{k=1..n} A284900(k)*a(n-k) for n > 0. - Seiichi Manyama, Apr 06 2017