A354891 a(n) = n! * Sum_{d|n} d^(n - d) / d!.

1, 3, 7, 73, 121, 9721, 5041, 1760641, 44452801, 562615201, 39916801, 3156125575681, 6227020801, 192873372531841, 222245415808416001, 14806216643368550401, 355687428096001, 34884164976924636172801, 121645100408832001

Offset: 1

Author

Seiichi Manyama, Jun 10 2022

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..305

Crossrefs

Cf. A038507, A342628, A354888, A354890, A354893.

Programs

Mathematica

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

PARI

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

PARI

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

Formula

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

If p is prime, a(p) = 1 + p! = A038507(p).