A363614 Expansion of Sum_{k>0} x^(2*k)/(1+x^k)^6.

0, 1, -6, 22, -56, 121, -252, 484, -798, 1232, -2002, 3145, -4368, 5937, -8630, 12112, -15504, 19678, -26334, 34902, -42762, 51129, -65780, 84337, -98336, 114388, -143304, 175869, -201376, 230120, -278256, 336744, -379000, 420394, -502250, 598459, -658008, 723065, -855042, 997962, -1086008

Offset

1,3

Links

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

Formula

G.f.: Sum_{k>0} binomial(k+3,5) * (-x)^k/(1 - x^k).

a(n) = Sum_{d|n} (-1)^d * binomial(d+3,5).

Mathematica

a[n_] := DivisorSum[n, (-1)^#*Binomial[# + 3, 5] &]; Array[a, 40] (* Amiram Eldar, Jul 18 2023 *)

Prog

(PARI) my(N=50, x='x+O('x^N)); concat(0, Vec(sum(k=1, N, x^(2*k)/(1+x^k)^6)))
(PARI) a(n) = sumdiv(n, d, (-1)^d*binomial(d+3, 5));

Crossrefs

Cf. A325940, A363022, A363598, A363613.

Cf. A363606.

Sequence in context: A212692 A034134 A081441 * A363606 A366448 A127760

Adjacent sequences: A363611 A363612 A363613 * A363615 A363616 A363617

Keyword

sign

Author

Seiichi Manyama, Jun 11 2023

Status

approved