A306691 Expansion of Product_{k>=1} (1 + x^k * (1 - x)).

1, 1, 0, 1, -1, 1, 0, -1, 1, 0, 0, -2, 4, -4, 3, -2, 0, 2, -1, -2, 3, -1, -3, 8, -11, 10, -8, 9, -13, 15, -9, -2, 6, 2, -14, 21, -20, 10, 8, -25, 29, -22, 20, -31, 46, -53, 48, -33, 15, -9, 27, -57, 71, -62, 53, -63, 83, -87, 53, 16, -80, 91, -47, 3, -19, 99, -186, 219, -184

Offset: 0

Author

Seiichi Manyama, Apr 16 2019

Keywords

• sign

Links

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

Crossrefs

Cf. A160571, A198197, A306565, A306749.

Programs

Mathematica

With[{nn=70},CoefficientList[Series[Product[1+x^k (1-x),{k,nn}],{x,0,nn}],x]] (* Harvey P. Dale, Aug 03 2020 *)

PARI

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

Formula

G.f.: exp(Sum_{k>=1} x^k * Sum_{d|k} (-1)^(d+1)*(1 - x)^d/d). - Ilya Gutkovskiy, Apr 16 2019