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Irregular triangle with T(n,1) = floor(n!/3), T(n,2) = n!/2, T(n,3) = n!, read by rows.
1

%I #7 May 12 2013 03:11:41

%S 1,1,2,2,3,6,8,12,24,40,60,120,240,360,720,1680,2520,5040,13440,20160,

%T 40320,120960,181440,362880,1209600,1814400,3628800

%N Irregular triangle with T(n,1) = floor(n!/3), T(n,2) = n!/2, T(n,3) = n!, read by rows.

%F T(n,1) = A002301(n), n>=3. T(n,2) = A001710(n). T(n,3) = A000142(n).

%e 1, 1, 2;

%e 2, 3, 6;

%e 8, 12, 24;

%e 40, 60, 120;

%e 240, 360, 720;

%e 1680, 2520, 5040;

%e 13440, 20160, 40320;

%e 120960, 181440, 362880;

%e 1209600, 1814400, 3628800;

%t Flatten[Table[{If[n < 3, 1, n!/3], If[n < 2, 1, n!/2], n!}, {n, 1, 10}]]

%K nonn,tabf,easy

%O 2,3

%A _Roger L. Bagula_, Jun 07 2007