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A307602 Expansion of Product_{k>=1} (1 + x^k/(1 + x)). 5

%I #14 Sep 16 2019 07:45:59

%S 1,1,0,2,-1,4,-2,5,-1,4,3,-2,16,-21,47,-62,104,-131,191,-229,304,-344,

%T 420,-437,477,-413,336,-76,-270,927,-1792,3155,-4904,7402,-10519,

%U 14694,-19761,26226,-33847,43162,-53776,66178,-79679,94562,-109606,124618,-137468,147061

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

%H Seiichi Manyama, <a href="/A307602/b307602.txt">Table of n, a(n) for n = 0..500</a>

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

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

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

%o (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)))))

%Y Cf. A126348, A307599, A307601.

%K sign

%O 0,4

%A _Seiichi Manyama_, Apr 18 2019

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