A363631 Expansion of Sum_{k>0} (1/(1+x^k)^4 - 1).

-4, 6, -24, 41, -60, 70, -124, 206, -244, 236, -368, 560, -564, 566, -896, 1175, -1144, 1180, -1544, 2042, -2168, 1942, -2604, 3650, -3336, 3100, -4304, 5096, -4964, 4940, -5988, 7720, -7528, 6636, -8616, 10809, -9884, 9126, -12064, 14548, -13248, 12796, -15184, 18192, -18412, 15830

Offset

1,1

Links

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

Formula

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

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

Mathematica

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

Prog

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

Crossrefs

Cf. A363629, A363630.

Cf. A320901, A363598, A363616, A363617.

Sequence in context: A305381 A164532 A098660 * A122174 A283185 A034458

Adjacent sequences: A363628 A363629 A363630 * A363632 A363633 A363634

Keyword

sign,easy

Author

Seiichi Manyama, Jun 12 2023

Status

approved