A363647 Expansion of Sum_{k>0} (1/(1 - (k*x)^k)^3 - 1).

3, 18, 91, 879, 9396, 145010, 2470665, 50728749, 1162458352, 30058615320, 855935011911, 26761537897338, 908625319776864, 33340089815701086, 1313681976619686558, 55341921135416377497, 2481720785659010292702, 118040125809311823596960

Offset

1,1

Links

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

Formula

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

Mathematica

a[n_] := DivisorSum[n, (n/#)^n * Binomial[# + 2, 2] &]; Array[a, 20] (* Amiram Eldar, Jul 17 2023 *)

Prog

(PARI) a(n) = sumdiv(n, d, (n/d)^n*binomial(d+2, 2));

Crossrefs

Cf. A023887, A338663, A363646, A363648.

Cf. A363639.

Sequence in context: A272492 A092691 A064671 * A058409 A125833 A129547

Adjacent sequences: A363644 A363645 A363646 * A363648 A363649 A363650

Keyword

nonn

Author

Seiichi Manyama, Jun 13 2023

Status

approved