A354845 a(n) = n! * Sum_{d|n} (n/d)^(d-1) / d!.

1, 3, 7, 49, 121, 2281, 5041, 134401, 907201, 13184641, 39916801, 3753509761, 6227020801, 393409336321, 7638997766401, 160474477363201, 355687428096001, 75792615407308801, 121645100408832001, 32459310892353945601, 475723576423839744001, 7306033564948620902401

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..447

Formula

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

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

Mathematica

a[n_] := n! * DivisorSum[n, (n/#)^(#-1)/#! &]; Array[a, 20] (* Amiram Eldar, Jun 08 2022 *)

Prog

(PARI) a(n) = n!*sumdiv(n, d, (n/d)^(d-1)/d!);
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, (exp(k*x^k)-1)/k)))

Crossrefs

Cf. A087906, A327578, A354843.

Sequence in context: A019039 A077559 A330020 * A327578 A358593 A062959

Adjacent sequences: A354842 A354843 A354844 * A354846 A354847 A354848

Keyword

nonn

Author

Seiichi Manyama, Jun 08 2022

Status

approved