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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.
2
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
KEYWORD
easy,nonn,tabl,nice
AUTHOR
Floor van Lamoen, Dec 23 2001
STATUS
approved