A307602 Expansion of Product_{k>=1} (1 + x^k/(1 + x)).

1, 1, 0, 2, -1, 4, -2, 5, -1, 4, 3, -2, 16, -21, 47, -62, 104, -131, 191, -229, 304, -344, 420, -437, 477, -413, 336, -76, -270, 927, -1792, 3155, -4904, 7402, -10519, 14694, -19761, 26226, -33847, 43162, -53776, 66178, -79679, 94562, -109606, 124618, -137468, 147061

Offset: 0

Author

Seiichi Manyama, Apr 18 2019

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A126348, A307599, A307601.

Programs

Mathematica

nmax = 50; CoefficientList[Series[Product[(1 + x + x^k)/(1 + x), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Sep 16 2019 *)

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)^(d+1)/(d*(1+x)^d)))))

Formula

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