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Triangle read by rows: t(n,k)=n!/(n - k*(n - k)).
0

%I #3 Mar 30 2012 17:34:33

%S 1,1,1,1,2,1,1,6,6,1,1,24,24,24,1,1,120,0,0,120,1,1,720,0,0,0,720,1,1,

%T 5040,0,0,0,0,5040,1,1,40320,0,0,0,0,0,40320,1,1,362880,0,0,0,0,0,0,

%U 362880,1,1,3628800,0,0,0,0,0,0,0,3628800,1

%N Triangle read by rows: t(n,k)=n!/(n - k*(n - k)).

%C Row sums are: {1, 2, 4, 14, 74, 242, 1442, 10082, 80642, 725762, 7257602,...}.

%C Second column is n!.

%e {1},

%e {1, 1},

%e {1, 2, 1},

%e {1, 6, 6, 1},

%e {1, 24, 24, 24, 1},

%e {1, 120, 0, 0, 120, 1},

%e {1, 720, 0, 0, 0, 720, 1},

%e {1, 5040, 0, 0, 0, 0, 5040, 1},

%e {1, 40320, 0, 0, 0, 0, 0, 40320, 1},

%e {1, 362880, 0, 0, 0, 0, 0, 0, 362880, 1},

%e {1, 3628800, 0, 0, 0, 0, 0, 0, 0, 3628800, 1}

%t Table[Table[n!/(n - k*(n - k))!, {k, 0, n}], {n, 0, 10}];

%t Flatten[%]

%K nonn,tabl

%O 0,5

%A _Roger L. Bagula_, Jan 27 2009

%E Edited by _N. J. A. Sloane_, Jan 31 2009