A363630 Expansion of Sum_{k>0} (1/(1+x^k)^3 - 1).

-3, 3, -13, 18, -24, 21, -39, 63, -68, 48, -81, 127, -108, 87, -170, 216, -174, 156, -213, 294, -302, 201, -303, 497, -375, 276, -474, 537, -468, 426, -531, 777, -686, 462, -726, 965, -744, 573, -938, 1200, -906, 798, -993, 1251, -1306, 831, -1179, 1875, -1314, 1023, -1562, 1722, -1488, 1290, -1698

Offset: 1

Author

Seiichi Manyama, Jun 12 2023

Keywords

• sign
• easy

Links

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

Crossrefs

Cf. A002129, A048272, A321543, A363629, A363631.

Cf. A320900, A363022, A363615.

Programs

Mathematica

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

PARI

a(n) = sumdiv(n, d, (-1)^d*binomial(d+2, 2));

Formula

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

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

a(n) = -(A321543(n) + 3*A002129(n) + 2*A048272(n)) / 2. - Amiram Eldar, Jan 04 2025