A363695 Expansion of Sum_{k>0} (1/(1-x^k)^5 - 1).

5, 20, 40, 90, 131, 265, 335, 585, 755, 1147, 1370, 2155, 2385, 3410, 4042, 5430, 5990, 8295, 8860, 11843, 13020, 16335, 17555, 23125, 23882, 29805, 32220, 39440, 40925, 51644, 52365, 64335, 67450, 79820, 82712, 101575, 101275, 120805, 125830, 148089, 149000, 179490

Offset

1,1

Links

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

Formula

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

a(n) = Sum_{d|n} binomial(d+4,4).

Mathematica

a[n_] := DivisorSum[n, Binomial[# + 4, 4] &]; Array[a, 40] (* Amiram Eldar, Jul 05 2023 *)

Prog

(PARI) a(n) = sumdiv(n, d, binomial(d+4, 4));

Crossrefs

Cf. A007503, A116963, A363628, A363696.

Cf. A073570, A363605, A363608.

Sequence in context: A161445 A238100 A031304 * A228168 A178977 A061188

Adjacent sequences: A363692 A363693 A363694 * A363696 A363697 A363698

Keyword

nonn,easy

Author

Seiichi Manyama, Jun 16 2023

Status

approved