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

%I #6 Feb 02 2024 16:13:12

%S 1,2,6,24,120,696,4536,32568,254136,2133816,19130040,182000952,

%T 1828296888,19311334200,213709376184,2470302259512,29746381049016,

%U 372270346391352,4831940144914104,64925998174811448,901626111996723384,12920858504042924856

%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.

%p g:= proc(n) option remember; `if` (n=0, 1, (1+add(binomial (n-1, k-1) * g(n-k), k=1..n-1)) * 4) end:

%p a:= n-> `if`(n<=1, n+1, 6*g(n-2)): seq (a(n), n=0..25); # _Sean A. Irvine_, Feb 02 2024

%Y Cf. A000110, A001861, A068199, this, A068201, ..., A000142.

%K nonn

%O 0,2

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

%E More terms from _Sean A. Irvine_, Feb 02 2024