A309575 Expansion of Product_{k>=1} (1 - (x*(1 + x))^k).

1, -1, -2, -2, -1, 1, 5, 11, 17, 26, 36, 35, 20, -5, -65, -221, -510, -897, -1379, -2157, -3498, -5225, -6500, -6425, -4775, -1463, 5951, 25905, 74833, 173129, 334719, 563200, 876876, 1363232, 2208921, 3621969, 5631470, 7896109, 9725768, 10374574, 9340382, 6104500, -1413334

Offset

0,3

Links

Table of n, a(n) for n=0..42.

Formula

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

Mathematica

nmax = 40; CoefficientList[Series[Product[(1 - (x*(1+x))^k), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Sep 22 2019 *)

Prog

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

Crossrefs

Convolution inverse of A238441.

Cf. A266108, A306565, A307501, A307548, A327671.

Sequence in context: A177694 A092450 A279629 * A014291 A136587 A136247

Adjacent sequences: A309572 A309573 A309574 * A309576 A309577 A309578

Keyword

sign

Author

Seiichi Manyama, Sep 21 2019

Status

approved