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A143216 Triangle read by rows: T(n,k) = n!*k!, 0 <= k <= n. 5

%I #17 Jul 12 2022 08:39:35

%S 1,1,1,2,2,4,6,6,12,36,24,24,48,144,576,120,120,240,720,2880,14400,

%T 720,720,1440,4320,17280,86400,518400,5040,5040,10080,30240,120960,

%U 604800,3628800,25401600,40320,40320,80640,241920,967680,4838400,29030400,203212800,1625702400

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

%H Stefano Spezia, <a href="/A143216/b143216.txt">First 101 rows of the triangle, flattened</a>

%F T(n,k) = n!*k!, 0 <= k <= n.

%F E.g.f.: 1/((1 - x)*(1 - y)). - _Stefano Spezia_, Jul 09 2020

%e First few rows of the triangle =

%e 1;

%e 1, 1;

%e 2, 2, 4;

%e 6, 6, 12, 36;

%e 24, 24, 48, 144, 576;

%e 120, 120, 240, 720, 2880, 14400;

%e 720, 720, 1440, 4320, 17280, 86400, 518400;

%e ...

%e T(6,3) = 4320 = 6!*3! = 720*6.

%t Table[n!k!,{n,0,8},{k,0,n}] (* _Stefano Spezia_, Jul 09 2020 *)

%o (Magma) F:=Factorial; [F(n)*F(k): k in [0..n], n in [0..12]]; // _G. C. Greubel_, Jul 12 2022

%o (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 Cf. A000142, A098361 (as an array), A143217 (row sums).

%K nonn,tabl

%O 0,4

%A _Gary W. Adamson_, Jul 30 2008

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Last modified March 28 22:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)