A068201 One of a family of sequences that interpolates between the Bell numbers and the factorials.

1, 2, 6, 24, 120, 720, 4920, 37320, 309120, 2763720, 26440920, 268864320, 2889978120, 32689371720, 387638491920, 4803456571320, 62026296732120, 832595493624720, 11592967532632920, 167119530011233320, 2489936579950221120, 38283169922493447720

Offset: 0

Author

N. J. A. Sloane, Mar 23 2002

Keywords

• nonn

References

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

Crossrefs

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

Programs

Maple

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

Extensions

More terms from Sean A. Irvine, Feb 02 2024