A068199 One of a family of sequences that interpolates between the Bell numbers and the factorials.

1, 2, 6, 24, 114, 618, 3732, 24702, 177126, 1363740, 11195286, 97437138, 894857712, 8637708858, 87333790686, 922203924216, 10144109299146, 115972625504994, 1375221840671220, 16884112119546534, 214270296662325534, 2806600053170775372, 37892025089041181982

Offset: 0

Author

N. J. A. Sloane, Mar 23 2002

Keywords

• nonn

References

• G. Labelle et al., Stirling numbers interpolation using permutations with forbidden subsequences, Discrete Math. 246 (2002), 177-195.

Crossrefs

Cf. A000110, A001861, this, A068200, A068201, ..., A000142.

Equals 2 * A027710(n).

Programs

Maple

g:= proc(n) option remember; `if`(n=0, 1,
      (1+add(binomial(n-1, k-1)*g(n-k), k=1..n-1))*3)
    end:
a:= n-> `if`(n=0, 1, 2*g(n-1)):
seq(a(n), n=0..25);  # Alois P. Heinz, Oct 09 2008

Mathematica

a[n_] := 2*BellB[n-1, 3]; a[0] = 1; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Nov 28 2014 *)

Formula

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

Extensions

More terms from Alois P. Heinz, Oct 09 2008