A354278 Product_{n>=1} 1 / (1 - a(n)*x^n/n!) = exp(-x) / (1 - x).

0, 1, 2, 3, 24, 50, 720, 4095, 35840, 267624, 3628800, 35724150, 479001600, 5240149200, 82614884352, 1188272460375, 20922789888000, 320893244672000, 6402373705728000, 113803149223980216, 2379913632645120000, 46396417566975840000, 1124000727777607680000

Offset

1,3

Links

Table of n, a(n) for n=1..23.

Formula

a(1) = 0; a(n) = (n-1)! * (1 - Sum_{d|n, 1 < d < n} d * (a(d)/d!)^(n/d)).

Mathematica

a[1] = 0; a[n_] := a[n] = (n - 1)! (1 - Sum[d (a[d]/d!)^(n/d), {d, Divisors[n]~Complement~{1, n}}]); Table[a[n], {n, 1, 23}]

Crossrefs

Cf. A000166, A006973, A137852, A353822, A354277.

Sequence in context: A092049 A257789 A336616 * A061778 A160667 A118204

Adjacent sequences: A354275 A354276 A354277 * A354279 A354280 A354281

Keyword

nonn

Author

Ilya Gutkovskiy, May 22 2022

Status

approved