A363615 Expansion of Sum_{k>0} x^(3*k)/(1+x^k)^3.

0, 0, 1, -3, 6, -9, 15, -24, 29, -30, 45, -67, 66, -63, 98, -129, 120, -117, 153, -204, 206, -165, 231, -341, 282, -234, 354, -417, 378, -354, 435, -594, 542, -408, 582, -770, 630, -513, 770, -966, 780, -702, 861, -1071, 1072, -759, 1035, -1527, 1143, -930, 1346

Offset

1,4

Links

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

Formula

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

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

Mathematica

a[n_] := -DivisorSum[n, (-1)^#*Binomial[# - 1, 2] &]; Array[a, 50] (* Amiram Eldar, Jul 18 2023 *)

Prog

(PARI) my(N=60, x='x+O('x^N)); concat([0, 0], Vec(sum(k=1, N, x^(3*k)/(1+x^k)^3)))
(PARI) a(n) = -sumdiv(n, d, (-1)^d*binomial(d-1, 2));

Crossrefs

Cf. A325940, A363616.

Cf. A363610.

Sequence in context: A364017 A352733 A112773 * A357989 A070885 A002597

Adjacent sequences: A363612 A363613 A363614 * A363616 A363617 A363618

Keyword

sign

Author

Seiichi Manyama, Jun 11 2023

Status

approved