A338689 a(n) = Sum_{d|n} (-1)^(d-1) * (n/d)^n * binomial(d+n/d-2, d-1).

1, 3, 28, 223, 3126, 44660, 823544, 16514047, 387538588, 9951176994, 285311670612, 8903202187413, 302875106592254, 11107259264162760, 437894348359764856, 18444492187995996159, 827240261886336764178, 39345059356329821149097

Offset

1,2

Links

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

Formula

G.f.: Sum_{k>=1} (k * x/(1 + (k * x)^k))^k.

If p is prime, a(p) = (-1)^(p-1) + p^p.

Mathematica

a[n_] := DivisorSum[n, (-1)^(# - 1) * (n/#)^n * Binomial[# + n/# - 2, # - 1] &]; Array[a, 20] (* Amiram Eldar, Apr 24 2021 *)

Prog

(PARI) a(n) = sumdiv(n, d, (-1)^(d-1)*(n/d)^n*binomial(d+n/d-2, d-1));
(PARI) N=20; x='x+O('x^N); Vec(sum(k=1, N, (k*x/(1+(k*x)^k))^k))

Crossrefs

Cf. A217670, A338661, A338684, A338688.

Sequence in context: A003466 A337590 A092637 * A094296 A172241 A321438

Adjacent sequences: A338686 A338687 A338688 * A338690 A338691 A338692

Keyword

nonn

Author

Seiichi Manyama, Apr 24 2021

Status

approved