A306565 Expansion of Product_{k>=1} (1 - x^k * (1 + x)).

1, -1, -2, -1, 1, 3, 4, 3, 1, -2, -6, -8, -8, -8, -5, 2, 8, 12, 17, 22, 23, 17, 7, 0, -7, -22, -40, -51, -53, -49, -45, -42, -30, -4, 30, 65, 90, 100, 112, 137, 157, 152, 120, 71, 18, -33, -80, -125, -187, -275, -357, -401, -407, -380, -327, -269, -221, -171, -75, 102, 322, 515, 669, 801

Offset: 0

Author

Seiichi Manyama, Apr 16 2019

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000

Crossrefs

Convolution inverse of A227681.

Cf. A160571.

Programs

Mathematica

m = 63; CoefficientList[Series[Product[1 - x^k * (1 + x), {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^k*(1+x)))

PARI

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

Formula

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