A354888 a(n) = n! * Sum_{d|n} d^d / d!.

1, 6, 33, 328, 3245, 52056, 828583, 17328256, 389416329, 10105386400, 285351587411, 8955841614336, 302881333613053, 11126513414294656, 437935136609883375, 18455736024587862016, 827240617573764860177, 39353706314004951028224

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..386

Formula

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

If p is prime, a(p) = p^p + p! = A053042(p).

Mathematica

a[n_] := n! * DivisorSum[n, #^#/#! &]; Array[a, 18] (* Amiram Eldar, Jun 10 2022 *)

Prog

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

Crossrefs

Cf. A327579, A354843, A354889.

Sequence in context: A118094 A343567 A306182 * A358595 A121376 A354890

Adjacent sequences: A354885 A354886 A354887 * A354889 A354890 A354891

Keyword

nonn

Author

Seiichi Manyama, Jun 10 2022

Status

approved