A363648 Expansion of Sum_{k>0} (1/(1 - (k*x)^k)^4 - 1).

4, 26, 128, 1219, 12556, 195278, 3294292, 67773349, 1550075836, 40097713880, 1141246682808, 35686524105658, 1211500426369572, 44454809534927314, 1751576172678539608, 73789791194939982793, 3308961047545347057848, 157387135278770854655312

Offset

1,1

Links

Table of n, a(n) for n=1..18.

Formula

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

Mathematica

a[n_] := DivisorSum[n, (n/#)^n * Binomial[# + 3, 3] &]; Array[a, 20] (* Amiram Eldar, Jul 17 2023 *)

Prog

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

Crossrefs

Cf. A023887, A338663, A363646, A363647.

Cf. A363640.

Sequence in context: A211166 A245460 A261738 * A184263 A058408 A053906

Adjacent sequences: A363645 A363646 A363647 * A363649 A363650 A363651

Keyword

nonn

Author

Seiichi Manyama, Jun 13 2023

Status

approved