A363613 Expansion of Sum_{k>0} x^(2*k)/(1+x^k)^5.

0, 1, -5, 16, -35, 66, -126, 226, -335, 461, -715, 1082, -1365, 1695, -2420, 3286, -3876, 4581, -5985, 7791, -8986, 9912, -12650, 16242, -17585, 19111, -24086, 29115, -31465, 34106, -40920, 49662, -53080, 55030, -66206, 79412, -82251, 85406, -102640, 119931

Offset

1,3

Links

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

Formula

G.f.: Sum_{k>0} binomial(k+2,4) * (-x)^k/(1 - x^k).

a(n) = Sum_{d|n} (-1)^d * binomial(d+2,4).

Mathematica

a[n_] := DivisorSum[n, (-1)^# * Binomial[# + 2, 4] &]; Array[a, 40] (* Amiram Eldar, Jul 25 2023 *)

Prog

(PARI) my(N=50, x='x+O('x^N)); concat(0, Vec(sum(k=1, N, x^(2*k)/(1+x^k)^5)))
(PARI) a(n) = sumdiv(n, d, (-1)^d*binomial(d+2, 4));

Crossrefs

Cf. A325940, A363022, A363598, A363614.

Cf. A363605.

Sequence in context: A190970 A077415 A234362 * A363605 A108966 A321019

Adjacent sequences: A363610 A363611 A363612 * A363614 A363615 A363616

Keyword

sign

Author

Seiichi Manyama, Jun 11 2023

Status

approved