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A068199
One of a family of sequences that interpolates between the Bell numbers and the factorials.
3
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.
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: A375913 A324133 A171448 * A189846 A189283 A177522
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Mar 23 2002
EXTENSIONS
More terms from Alois P. Heinz, Oct 09 2008
STATUS
approved