A343567 a(n) = Sum_{d|n} (n/d)^(n/d) * binomial(d+n-2,n-1).

1, 6, 33, 292, 3195, 47154, 824467, 16783176, 387434574, 10000082730, 285311855367, 8916101760828, 302875109296409, 11112006847596746, 437893890421433595, 18446744074133995664, 827240261886937844567, 39346408075305857765940

Offset

1,2

Links

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

Formula

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

Mathematica

a[n_] := DivisorSum[n, (n/#)^(n/#) * Binomial[# + n - 2, n - 1] &]; Array[a, 20] (* Amiram Eldar, Apr 25 2021 *)

Prog

(PARI) a(n) = sumdiv(n, d, (n/d)^(n/d)*binomial(d+n-2, n-1));

Crossrefs

Cf. A062796, A343547, A343568.

Sequence in context: A228640 A228618 A118094 * A306182 A354888 A358595

Adjacent sequences: A343564 A343565 A343566 * A343568 A343569 A343570

Keyword

nonn

Author

Seiichi Manyama, Apr 20 2021

Status

approved