A336999 a(n) = n! * Sum_{d|n} n^d / d!.

1, 8, 45, 544, 3725, 89856, 858823, 25271296, 434776329, 13241728000, 285750755411, 11494661861376, 302956057862653, 12945137688641536, 446924199188379375, 20735627677666902016, 827246308572614396177, 43155924331583693389824

Offset: 1

Author

Ilya Gutkovskiy, Aug 10 2020

Keywords

• nonn

Crossrefs

Cf. A057625, A063170, A066108.

Programs

Mathematica

Table[n! Sum[n^d/d!, {d, Divisors[n]}], {n, 1, 18}]
Table[n! SeriesCoefficient[Sum[(Exp[n x^k] - 1), {k, 1, n}], {x, 0, n}], {n, 1, 18}]

PARI

a(n) = n! * sumdiv(n, d, n^d/d!); \\ Michel Marcus, Aug 12 2020

Formula

a(n) = n! * [x^n] Sum_{k>=1} (exp(n*x^k) - 1).