A363611 - OEIS

A363611

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

0, 0, 0, 1, 4, 10, 20, 36, 56, 88, 120, 176, 220, 306, 368, 491, 560, 746, 816, 1058, 1160, 1450, 1540, 1982, 2028, 2520, 2656, 3232, 3276, 4116, 4060, 4986, 5080, 6016, 6008, 7457, 7140, 8586, 8656, 10232, 9880, 12116, 11480, 13792, 13668, 15730, 15180, 18652, 17316, 20536

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OFFSET

1,5

LINKS

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

FORMULA

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

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

MATHEMATICA

a[n_] := DivisorSum[n, Binomial[# - 1, 3] &]; Array[a, 50] (* Amiram Eldar, Jul 25 2023 *)

PROG

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