A307548 Expansion of Product_{k>=1} (1 - (x/(1+x))^k).

1, -1, 0, 1, -2, 4, -9, 21, -48, 105, -218, 429, -803, 1442, -2521, 4380, -7734, 14091, -26468, 50405, -94980, 172824, -296704, 467589, -644459, 678109, -177123, -1752141, 7003180, -19432494, 46778567, -104623822, 224830880, -473859273, 992825436, -2084921584

Offset: 0

Author

Seiichi Manyama, Apr 14 2019

Keywords

• sign
• easy

Crossrefs

Convolution inverse of A320590.

Cf. A129519, A307310, A320591.

Programs

Mathematica

m = 35; CoefficientList[Series[Product[1 - (x/(1+x))^k, {k, 1, m}], {x, 0, m}], x] (* Amiram Eldar, May 14 2021 *)

PARI

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

Formula

O.g.f.: Sum_{n >= 0} (-1)^n * x^(n*(n+1)/2)/Product_{k = 1..n} ((1 + x)^k - x^k). Cf. A320591. - Peter Bala, Dec 22 2020