A363617 Expansion of Sum_{k>0} x^(3*k)/(1+x^k)^4.

0, 0, 1, -4, 10, -19, 35, -60, 85, -110, 165, -243, 286, -329, 466, -620, 680, -751, 969, -1254, 1366, -1375, 1771, -2323, 2310, -2314, 3010, -3609, 3654, -3734, 4495, -5580, 5622, -5304, 6590, -8115, 7770, -7467, 9426, -11190, 10660, -10498, 12341, -14623, 14740, -13409, 16215, -20179, 18459, -17410, 21506

Offset: 1

Author

Seiichi Manyama, Jun 11 2023

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A363022, A363618.

Cf. A363607.

Programs

Mathematica

a[n_] := -DivisorSum[n, (-1)^#*Binomial[#, 3] &]; Array[a, 50] (* Amiram Eldar, Jul 18 2023 *)

PARI

my(N=60, x='x+O('x^N)); concat([0, 0], Vec(sum(k=1, N, x^(3*k)/(1+x^k)^4)))

PARI

a(n) = -sumdiv(n, d, (-1)^d*binomial(d, 3));

Formula

G.f.: -Sum_{k>0} binomial(k,3) * (-x)^k/(1 - x^k).

a(n) = -Sum_{d|n} (-1)^d * binomial(d,3).