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

1,3

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.

Formula

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

Example

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;
  ...

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 *)

Crossrefs

Row sums give A057625.

Main diagonal gives A000142.

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

Sequence in context: A122930 A364303 A364518 * A180663 A331327 A301924

Adjacent sequences: A066384 A066385 A066386 * A066388 A066389 A066390

Keyword

easy,nonn,tabl,nice

Author

Floor van Lamoen, Dec 23 2001

Status

approved