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

%I #7 Feb 02 2024 18:29:46

%S 1,2,6,24,120,720,4920,37320,309120,2763720,26440920,268864320,

%T 2889978120,32689371720,387638491920,4803456571320,62026296732120,

%U 832595493624720,11592967532632920,167119530011233320,2489936579950221120,38283169922493447720

%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)) * 5) end:

%p a:= n-> `if`(n<=2, (n+1)!, 24*g(n-3)): seq (a(n), n=0..25); # _Sean A. Irvine_, Feb 02 2024

%Y Cf. A000110, A001861, A068199, A068200, this, ..., A000142.

%K nonn

%O 0,2

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

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