A354890 a(n) = n! * Sum_{d|n} d^n / d!.

1, 6, 33, 472, 3245, 157896, 828583, 132078976, 1578211209, 307174074400, 285351587411, 1835340563252736, 302881333613053, 11743240652094910336, 336123967242674523375, 149825956013958069846016, 827240617573764860177, 3551697093896307129060647424

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..284

Formula

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

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

Mathematica

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

Prog

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

Crossrefs

Cf. A053042, A354888, A354891, A354892.

Sequence in context: A354888 A358595 A121376 * A046707 A337825 A183466

Adjacent sequences: A354887 A354888 A354889 * A354891 A354892 A354893

Keyword

nonn

Author

Seiichi Manyama, Jun 10 2022

Status

approved