A354899 - OEIS

A354899

a(n) = n! * Sum_{d|n} d^d / (d! * (n/d)!).

1, 5, 28, 281, 3126, 48517, 823544, 16995617, 387692650, 10047310481, 285311670612, 8932562801857, 302875106592254, 11119129387084097, 437899615088648176, 18451106376806703617, 827240261886336764178, 39349894934527426209025

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OFFSET

1,2

LINKS

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

FORMULA

E.g.f.: Sum_{k>0} k^k * (exp(x^k) - 1)/k!.

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

MATHEMATICA

a[n_] := n! * DivisorSum[n, #^#/(#! * (n/#)!) &]; Array[a, 18] (* Amiram Eldar, Jun 11 2022 *)

PROG

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

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, k^k*(exp(x^k)-1)/k!)))

CROSSREFS

Cf. A121860, A354844, A354888, A354897, A354900.

Sequence in context: A339712 A023887 A171187 * A057792 A338661 A174464

Adjacent sequences: A354896 A354897 A354898 * A354900 A354901 A354902

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Jun 11 2022

STATUS

approved