A336978 Expansion of Product_{k>=1} (1 - x^k * (1 + k*x)).

1, -1, -2, -2, 0, 3, 8, 11, 9, 8, -10, -31, -57, -58, -107, -85, -4, 120, 167, 383, 616, 905, 948, 479, -82, -125, -905, -3661, -5937, -8247, -8807, -7756, -6249, -8147, -3525, 8330, 30748, 54740, 82660, 85406, 86083, 109681, 148897, 148077, 81288, -57885, -257092, -490304

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 A336976.

Cf. A306565, A336975, A336978, A336979, A336980.

Programs

Mathematica

m = 47; CoefficientList[Series[Product[1 - x^k*(1 + 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*(1+k*x)))

PARI

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

Formula

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