A336991 Expansion of Product_{k>=1} (1 - x^k / (1 - k*x)).

1, -1, -2, -3, -5, -10, -27, -91, -350, -1459, -6466, -30258, -149051, -771157, -4181702, -23718221, -140437759, -866481074, -5561061327, -37066185842, -256190732502, -1833581728979, -13571059095383, -103744579461855, -818183156375886, -6649600332967494, -55635988924348030

Offset

0,3

Links

Table of n, a(n) for n=0..26.

Formula

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

Mathematica

m = 26; CoefficientList[Series[Product[(1 - x^k/(1 - k*x)), {k, 1, m}], {x, 0, m}], x] (* Amiram Eldar, Aug 10 2020 *)

Prog

(PARI) N=40; x='x+O('x^N); Vec(prod(k=1, N, 1-x^k/(1-k*x)))
(PARI) N=40; x='x+O('x^N); Vec(exp(-sum(k=1, N, x^k*sumdiv(k, d, 1/(d*(1-k/d*x)^d)))))

Crossrefs

Convolution inverse of A336990.

Cf. A307599, A336989.

Sequence in context: A296261 A133662 A204518 * A223545 A088938 A000617

Adjacent sequences: A336988 A336989 A336990 * A336992 A336993 A336994

Keyword

sign

Author

Seiichi Manyama, Aug 10 2020

Status

approved