A066387 Triangle T(n,m) (1<=m<=n) giving number of maps f:N -> N such that f^m(X)=X+n for all natural numbers X.

1, 1, 2, 1, 0, 6, 1, 12, 0, 24, 1, 0, 0, 0, 120, 1, 120, 360, 0, 0, 720, 1, 0, 0, 0, 0, 0, 5040, 1, 1680, 0, 20160, 0, 0, 0, 40320, 1, 0, 60480, 0, 0, 0, 0, 0, 362880, 1, 30240, 0, 0, 1814400, 0, 0, 0, 0, 3628800, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 39916800

Offset: 1

Author

Floor van Lamoen, Dec 23 2001

Keywords

• easy
• nonn
• tabl
• nice

Examples

			Triangle T(n,m) begins:
  1;
  1,    2;
  1,    0,   6;
  1,   12,   0,    24;
  1,    0,   0,     0, 120;
  1,  120, 360,     0,   0, 720;
  1,    0,   0,     0,   0,   0, 5040;
  1, 1680,   0, 20160,   0,   0,    0, 40320;
  ...
		

Links

• Vincenzo Librandi, Rows n = 1..100, flattened
• A. Heinis, R. Jeurissen and L. Kamstra, Problem 18 and solution, Nieuw Arch. Wisk. 5/2 (2001) 380.

Crossrefs

Row sums give A057625.

Main diagonal gives A000142.

m-section of column m=2-4 (for n>0) gives: A001813, A064350, A166338.

Programs

Mathematica

t[n_, m_] /; Divisible[n, m] := n!/(n/m)!; t[, ] = 0; Flatten[Table[t[n, m], {n, 1, 11}, {m, 1, n}]] (* Jean-François Alcover, Nov 29 2011 *)

Formula

T(n,m) = n!/(n/m)! if m|n, T(n,m) = 0 otherwise.