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%I #18 Jul 25 2023 17:17:19
%S 0,1,-5,16,-35,66,-126,226,-335,461,-715,1082,-1365,1695,-2420,3286,
%T -3876,4581,-5985,7791,-8986,9912,-12650,16242,-17585,19111,-24086,
%U 29115,-31465,34106,-40920,49662,-53080,55030,-66206,79412,-82251,85406,-102640,119931
%N Expansion of Sum_{k>0} x^(2*k)/(1+x^k)^5.
%H Seiichi Manyama, <a href="/A363613/b363613.txt">Table of n, a(n) for n = 1..10000</a>
%F G.f.: Sum_{k>0} binomial(k+2,4) * (-x)^k/(1 - x^k).
%F a(n) = Sum_{d|n} (-1)^d * binomial(d+2,4).
%t a[n_] := DivisorSum[n, (-1)^# * Binomial[# + 2, 4] &]; Array[a, 40] (* _Amiram Eldar_, Jul 25 2023 *)
%o (PARI) my(N=50, x='x+O('x^N)); concat(0, Vec(sum(k=1, N, x^(2*k)/(1+x^k)^5)))
%o (PARI) a(n) = sumdiv(n, d, (-1)^d*binomial(d+2, 4));
%Y Cf. A325940, A363022, A363598, A363614.
%Y Cf. A363605.
%K sign
%O 1,3
%A _Seiichi Manyama_, Jun 11 2023
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