A354889 a(n) = n! * Sum_{d|n} d^(d-1) / d!.

1, 4, 15, 112, 745, 10296, 122689, 2285312, 43953921, 1026157600, 25977341401, 751135431168, 23304312143281, 795924137531264, 29203006015310625, 1154107395053387776, 48661547563094964481, 2186762596692631699968, 104127471943011650364841

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..387

Formula

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

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

Mathematica

a[n_] := n! * DivisorSum[n, #^(# - 1)/#! &]; Array[a, 19] (* Amiram Eldar, Jun 10 2022 *)

Prog

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

Crossrefs

Cf. A262843, A327578, A354845, A354888.

Sequence in context: A350484 A303654 A027162 * A197703 A352608 A136506

Adjacent sequences: A354886 A354887 A354888 * A354890 A354891 A354892

Keyword

nonn

Author

Seiichi Manyama, Jun 10 2022

Status

approved