A368765 a(n) = n! * (1 + Sum_{k=0..n} (-1)^k * k / k!).

1, 0, 2, 3, 16, 75, 456, 3185, 25488, 229383, 2293840, 25232229, 302786760, 3936227867, 55107190152, 826607852265, 13225725636256, 224837335816335, 4047072044694048, 76894368849186893, 1537887376983737880, 32295634916658495459, 710503968166486900120, 16341591267829198702737

Offset: 0

Author

Seiichi Manyama, Jan 04 2024

Keywords

• nonn

Crossrefs

Cf. A368766, A368767, A368768.

Cf. A000240, A033540.

Programs

Mathematica

Table[n!(1+Sum[(-1)^k k/k!,{k,0,n}]),{n,0,30}] (* Harvey P. Dale, Mar 26 2025 *)

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace((1-x*exp(-x))/(1-x)))

Formula

a(0) = 1; a(n) = n*a(n-1) + (-1)^n * n.

a(n) = n! - A000240(n).

E.g.f.: (1 - x * exp(-x)) / (1-x).

a(n) ~ (1 - exp(-1)) * n!. - Vaclav Kotesovec, Jan 13 2024