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A143216 Triangle read by rows: T(n,k) = n!*k!, 0 <= k <= n.

%I A143216 #17 Jul 12 2022 08:39:35
%S A143216 1,1,1,2,2,4,6,6,12,36,24,24,48,144,576,120,120,240,720,2880,14400,
%T A143216 720,720,1440,4320,17280,86400,518400,5040,5040,10080,30240,120960,
%U A143216 604800,3628800,25401600,40320,40320,80640,241920,967680,4838400,29030400,203212800,1625702400
%N A143216 Triangle read by rows: T(n,k) = n!*k!, 0 <= k <= n.
%H A143216 Stefano Spezia, <a href="/A143216/b143216.txt">First 101 rows of the triangle, flattened</a>
%F A143216 T(n,k) = n!*k!, 0 <= k <= n.
%F A143216 E.g.f.: 1/((1 - x)*(1 - y)). - _Stefano Spezia_, Jul 09 2020
%e A143216 First few rows of the triangle =
%e A143216     1;
%e A143216     1,   1;
%e A143216     2,   2,    4;
%e A143216     6,   6,   12,   36;
%e A143216    24,  24,   48,  144,   576;
%e A143216   120, 120,  240,  720,  2880, 14400;
%e A143216   720, 720, 1440, 4320, 17280, 86400, 518400;
%e A143216   ...
%e A143216 T(6,3) = 4320 = 6!*3! = 720*6.
%t A143216 Table[n!k!,{n,0,8},{k,0,n}] (* _Stefano Spezia_, Jul 09 2020 *)
%o A143216 (Magma) F:=Factorial; [F(n)*F(k): k in [0..n], n in [0..12]]; // _G. C. Greubel_, Jul 12 2022
%o A143216 (SageMath) f=factorial; flatten([[f(n)*f(k) for k in (0..n)] for n in (0..12)]) # _G. C. Greubel_, Jul 12 2022
%Y A143216 Cf. A000142, A098361 (as an array), A143217 (row sums).
%K A143216 nonn,tabl
%O A143216 0,4
%A A143216 _Gary W. Adamson_, Jul 30 2008