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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 (list; table; graph; refs; listen; history; text; internal format)
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: A119275 A129462 A122930 * 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

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Last modified February 26 21:58 EST 2020. Contains 332295 sequences. (Running on oeis4.)