%I #16 Jul 20 2023 10:47:05

%S 1,1,15,-6,40,12,77,-60,180,30,187,-120,260,56,630,-376,442,117,551,

%T -340,1218,132,805,-1104,1325,182,1998,-672,1276,360,1457,-2032,2970,

%U 306,3290,-1710,2072,380,4134,-3080,2542,672,2795,-1672,7830,552,3337,-6816,4998,775,7038,-2340,4240,1080

%N Expansion of Sum_{k>0} k^2 * x^k/(1 + x^k)^3.

%H Seiichi Manyama, <a href="/A364351/b364351.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = (n/2) * Sum_{d|n} (-1)^(n/d+1) * (d+n) = (n/2) * (A000593(n) + n * A048272(n)).

%t a[n_] := DivisorSum[n, (-1)^(n/#+1) * (#+n) &] * n/2; Array[a, 55] (* _Amiram Eldar_, Jul 20 2023 *)

%o (PARI) my(N=60, x='x+O('x^N)); Vec(sum(k=1, N, k^2*x^k/(1+x^k)^3))

%Y Cf. A320900, A364343.

%Y Cf. A000593, A048272, A309732.

%K sign

%O 1,3

%A _Seiichi Manyama_, Jul 19 2023