A336977 Expansion of Product_{k>=1} (1 - x^k * (k + x)).

1, -1, -3, -2, 1, 9, 11, 15, 6, -18, -46, -54, -115, -101, 32, 82, 182, 455, 804, 915, 434, -114, 196, -974, -3507, -6913, -7555, -5081, -4480, -7463, -4861, 7677, 25779, 56080, 76015, 51021, 53996, 104670, 114132, 93920, -33843, -233380, -491936, -658774, -597698, -601576

Offset: 0

Author

Seiichi Manyama, Aug 09 2020

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000

Crossrefs

Convolution inverse of A336975.

Cf. A022661, A306565, A336976, A336978, A336979, A336980.

Programs

Mathematica

m = 45; CoefficientList[Series[Product[1 - x^k*(k + x), {k, 1, m}], {x, 0, m}], x] (* Amiram Eldar, May 01 2021 *)

PARI

N=66; x='x+O('x^N); Vec(prod(k=1, N, 1-x^k*(k+x)))

PARI

N=66; x='x+O('x^N); Vec(exp(-sum(k=1, N, x^k*sumdiv(k, d, (k/d+x)^d/d))))

Formula

G.f.: exp( - Sum_{k>=1} x^k * Sum_{d|k} (k/d + x)^d / d).