A354277 Product_{n>=1} 1 / (1 - x^n/n!)^a(n) = exp(-x) / (1 - x).

0, 1, 2, 3, 24, 70, 720, 4305, 39200, 337176, 3628800, 38417610, 479001600, 6128488080, 87104969952, 1297383162075, 20922789888000, 354250929192160, 6402373705728000, 121407227453840328, 2432849766865689600, 51041047393559059200, 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 * d!^(-n/d) * a(d)).

Mathematica

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

Crossrefs

Cf. A000166, A006973, A137852, A353822, A354278.

Sequence in context: A343566 A057665 A371480 * A157327 A174073 A009231

Adjacent sequences: A354274 A354275 A354276 * A354278 A354279 A354280

Keyword

nonn

Author

Ilya Gutkovskiy, May 22 2022

Status

approved