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One of a family of sequences that interpolates between the Bell numbers and the factorials.
3

%I #15 Feb 02 2024 16:33:27

%S 1,2,6,24,114,618,3732,24702,177126,1363740,11195286,97437138,

%T 894857712,8637708858,87333790686,922203924216,10144109299146,

%U 115972625504994,1375221840671220,16884112119546534,214270296662325534,2806600053170775372,37892025089041181982

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

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

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

%p g:= proc(n) option remember; `if`(n=0, 1,

%p (1+add(binomial(n-1, k-1)*g(n-k), k=1..n-1))*3)

%p end:

%p a:= n-> `if`(n=0, 1, 2*g(n-1)):

%p seq(a(n), n=0..25); # _Alois P. Heinz_, Oct 09 2008

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

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

%Y Equals 2 * A027710(n).

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Mar 23 2002

%E More terms from _Alois P. Heinz_, Oct 09 2008