A082427 a(1)=1, a(n) = n * (Sum_{k=1..n-1} a(k)) - 2.

1, 0, 1, 6, 38, 274, 2238, 20462, 207178, 2301978, 27853934, 364633318, 5135252562, 77423807858, 1244311197718, 21236244441054, 383579665216538, 7310577148832842, 146617686151591998, 3086688129507199958, 68061473255633759074, 1568654907415559018658

Offset: 1

Author

Benoit Cloitre, Apr 24 2003

Keywords

• nonn

Crossrefs

Cf. A007808, A074143, A082425, A082428, A082430, A383436, A383437.

Cf. A001339.

Programs

Mathematica

Join[{1},Table[Floor[n(11/2-2E)n!],{n,2,20}]] (* Harvey P. Dale, May 09 2013 *)

Formula

a(n) = floor(n*(11/2 - 2*e)*n!) for n >= 2.

a(n) = (n+2)*a(n-1) - (n-1)*a(n-2) for n>3. - Gary Detlefs, Jun 30 2024

From Seiichi Manyama, Apr 27 2025: (Start)

E.g.f.: 2 + 3*x/2 + (11*x/2 - 2*exp(x))/(1-x)^2.

a(n) = 11*n/2 * n! - 2 * Sum_{k=0..n} (k+1)! * binomial(n,k) for n > 1.

a(n) = (n^2 * a(n-1) + 2)/(n-1) for n > 2. (End)

Extensions

Offset changed to 1 by Georg Fischer, May 15 2024