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A143084 Triangle read by rows: T(n,m) = (n + m)!.

%I A143084 #18 Jul 12 2024 19:17:31
%S A143084 1,1,2,2,6,24,6,24,120,720,24,120,720,5040,40320,120,720,5040,40320,
%T A143084 362880,3628800,720,5040,40320,362880,3628800,39916800,479001600,5040,
%U A143084 40320,362880,3628800,39916800,479001600,6227020800,87178291200
%N A143084 Triangle read by rows: T(n,m) = (n + m)!.
%H A143084 Jinyuan Wang, <a href="/A143084/b143084.txt">Rows n = 0..50 of triangle, flattened</a>
%F A143084 T(n,m) = (n + m)!.
%e A143084 Triangle begins:
%e A143084     1;
%e A143084     1,    2;
%e A143084     2,    6,    24;
%e A143084     6,   24,   120,    720;
%e A143084    24,  120,   720,   5040,   40320;
%e A143084   120,  720,  5040,  40320,  362880,  3628800;
%e A143084   720, 5040, 40320, 362880, 3628800, 39916800, 479001600;
%e A143084   ...
%t A143084 t[n_, m_] := (n + m)!; Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[%]
%Y A143084 Column m=0 gives A000142.
%Y A143084 T(2n,n) gives A100732.
%Y A143084 Main diagonal gives A010050.
%Y A143084 Row sums give A374574.
%K A143084 nonn,easy,tabl
%O A143084 0,3
%A A143084 _Roger L. Bagula_ and _Gary W. Adamson_, Oct 16 2008
%E A143084 Offset changed to 0 by _Jinyuan Wang_, Dec 19 2020