A018933 From the game of Mousetrap.

2, 11, 50, 348, 2712, 23520, 225360, 2368800, 27135360, 336752640, 4503340800, 64585382400, 989138304000, 16115529830400, 278360283801600, 5081622594048000, 97772197146624000, 1977622100213760000

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Daniel J. Mundfrom, A problem in permutations: the game of 'Mousetrap'. European J. Combin. 15 (1994), no. 6, 555-560.

Crossrefs

Cf. A002468.

Programs

Maple

c := proc(n,x) local a,i; if n > x+1 then a := (n-2)! ; for i from 3 to x do a := a+(-1)^i*(binomial(x-2,i-2)+binomial(x-3,i-3))*(n-i)! ; od: fi; a ; end: A018933 := proc(n) if n = 5 then 2 ; elif n = 6 then 11 ; else c(n,5) ; fi: end: for n from 5 to 23 do printf("%d,",A018933(n)) ; od: # R. J. Mathar, Oct 02 2008

Mathematica

c[n_, x_] := Module[{a = 0, i}, If[n > x+1, a = (n-2)!; For[i = 3, i <= x, i++, a += (-1)^i (Binomial[x-2, i-2] + Binomial[x-3, i-3]) (n-i)!]]; a];
b[n_] := If[n == 5, 2, If[n == 6, 11, c[n, 5]]];
a[n_] := b[n + 5];
a /@ Range[0, 17] (* Jean-François Alcover, Apr 05 2020, after R. J. Mathar *)

Extensions

This entry was corrupted by a misplaced edit Nov 30 2007; previous (and correct) version restored by N. J. A. Sloane Jan 25 2008

More terms from R. J. Mathar, Oct 02 2008