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%I #27 May 22 2023 07:49:57
%S 1,4,3,10,12,6,20,30,24,10,35,60,60,40,15,56,105,120,100,60,21,84,168,
%T 210,200,150,84,28,120,252,336,350,300,210,112,36,165,360,504,560,525,
%U 420,280,144,45,220,495,720,840,840,735,560,360,180,55
%N Array A000292(n)*A000217(k), read by antidiagonals.
%H Isabel Cação, Helmuth R. Malonek, Maria Irene Falcão, and Graça Tomaz, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL26/Falcao/falcao5.html">Intrinsic Properties of a Non-Symmetric Number Triangle</a>, J. Int. Seq., Vol. 26 (2023), Article 23.4.8.
%F G.f.: x*y/((1 - x)^4*(1 - y)^3). - _Stefano Spezia_, May 21 2023
%e Array begins
%e 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...
%e 4, 12, 24, 40, 60, 84, 112, 144, 180, 220, ...
%e 10, 30, 60, 100, 150, 210, 280, 360, 450, 550, ...
%e 20, 60, 120, 200, 300, 420, 560, 720, 900, 1100, ...
%e 35, 105, 210, 350, 525, 735, 980, 1260, 1575, 1925, ...
%e ...
%t A[n_,k_]:=Binomial[n+2,3]Binomial[k+1,2]; Table[A[n-k+1,k],{n,10},{k,n}]//Flatten (* _Stefano Spezia_, May 21 2023 *)
%Y Cf. A000579 (antidiagonal sums).
%Y Main diagonal gives A004302.
%Y Cf. A000217, A000292.
%K nonn,tabl,easy
%O 1,2
%A _Gary W. Adamson_, Mar 20 2005
%E More terms from _Stefano Spezia_, May 21 2023
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