A363662 a(n) = Sum_{d|n} (n/d)^n * binomial(d+n,n).

2, 18, 128, 1590, 19002, 353304, 6591776, 154083654, 3878583770, 110647791078, 3423740752764, 116116072618104, 4240251502692142, 166761491097360240, 7006327371058071648, 313637735782416564806, 14890324713956395361406, 747610406539465959084870

Offset

1,1

Links

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

Formula

a(n) = [x^n] Sum_{k>0} (1/(1 - (k*x)^k)^(n+1) - 1).

Mathematica

a[n_] := DivisorSum[n, (n/#)^n * Binomial[# + n, n] &]; Array[a, 20] (* Amiram Eldar, Jul 12 2023 *)

Prog

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

Crossrefs

Cf. A363646, A363647, A363648.

Cf. A023887, A363660, A363661.

Sequence in context: A325275 A277661 A367553 * A064447 A043022 A057971

Adjacent sequences: A363659 A363660 A363661 * A363663 A363664 A363665

Keyword

nonn

Author

Seiichi Manyama, Jun 14 2023

Status

approved