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

0,2

References

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

Links

Table of n, a(n) for n=0..22.

Formula

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

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 *)

Crossrefs

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

Equals 2 * A027710(n).

Sequence in context: A134664 A324133 A171448 * A189846 A189283 A177522

Adjacent sequences: A068196 A068197 A068198 * A068200 A068201 A068202

Keyword

nonn

Author

N. J. A. Sloane, Mar 23 2002

Extensions

More terms from Alois P. Heinz, Oct 09 2008

Status

approved