A327671 Expansion of Product_{k>=1} (1 - (x*(1 - x))^k).

1, -1, 0, 2, -1, 1, -5, 11, -17, 26, -36, 35, -22, 19, -67, 219, -480, 687, -469, -573, 2508, -4785, 6370, -6445, 5235, -4543, 8681, -26815, 75043, -173159, 334721, -563200, 876876, -1363232, 2208921, -3621971, 5631540, -7897299, 9738858, -10479294, 9989646, -9350820

Offset

0,4

Links

Table of n, a(n) for n=0..41.

Formula

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

Mathematica

m = 41; CoefficientList[Series[Product[(1 - (x*(1 - x))^k), {k, 1, m}], {x, 0, m}], x] (* Amiram Eldar, May 07 2021 *)

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 A307500.

Cf. A307310, A307501.

Sequence in context: A006704 A324960 A174986 * A036563 A025264 A321716

Adjacent sequences: A327668 A327669 A327670 * A327672 A327673 A327674

Keyword

sign

Author

Seiichi Manyama, Sep 21 2019

Status

approved