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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 (list; graph; refs; listen; history; text; internal format)
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..20.

FORMULA

E.g.f.: 1 + 2exp(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-Fran├žois 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

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Last modified November 19 08:44 EST 2019. Contains 329318 sequences. (Running on oeis4.)