%I #21 Jul 19 2023 02:19:50
%S 0,0,1,-3,6,-9,15,-24,29,-30,45,-67,66,-63,98,-129,120,-117,153,-204,
%T 206,-165,231,-341,282,-234,354,-417,378,-354,435,-594,542,-408,582,
%U -770,630,-513,770,-966,780,-702,861,-1071,1072,-759,1035,-1527,1143,-930,1346
%N Expansion of Sum_{k>0} x^(3*k)/(1+x^k)^3.
%H Seiichi Manyama, <a href="/A363615/b363615.txt">Table of n, a(n) for n = 1..10000</a>
%F G.f.: -Sum_{k>0} binomial(k-1,2) * (-x)^k/(1 - x^k).
%F a(n) = -Sum_{d|n} (-1)^d * binomial(d-1,2).
%t a[n_] := -DivisorSum[n, (-1)^#*Binomial[# - 1, 2] &]; Array[a, 50] (* _Amiram Eldar_, Jul 18 2023 *)
%o (PARI) my(N=60, x='x+O('x^N)); concat([0, 0], Vec(sum(k=1, N, x^(3*k)/(1+x^k)^3)))
%o (PARI) a(n) = -sumdiv(n, d, (-1)^d*binomial(d-1, 2));
%Y Cf. A325940, A363616.
%Y Cf. A363610.
%K sign
%O 1,4
%A _Seiichi Manyama_, Jun 11 2023
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