A309575 Expansion of Product_{k>=1} (1 - (x*(1 + x))^k).
1, -1, -2, -2, -1, 1, 5, 11, 17, 26, 36, 35, 20, -5, -65, -221, -510, -897, -1379, -2157, -3498, -5225, -6500, -6425, -4775, -1463, 5951, 25905, 74833, 173129, 334719, 563200, 876876, 1363232, 2208921, 3621969, 5631470, 7896109, 9725768, 10374574, 9340382, 6104500, -1413334
Offset: 0
Keywords
Programs
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Mathematica
nmax = 40; CoefficientList[Series[Product[(1 - (x*(1+x))^k), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Sep 22 2019 *) -
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)))
Formula
G.f.: exp(-Sum_{k>=1} sigma(k)*(x*(1+x))^k/k).