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A103252 Array A000292(n)*A000217(k), read by antidiagonals.

%I A103252 #31 Apr 04 2025 15:29:26
%S A103252 1,4,3,10,12,6,20,30,24,10,35,60,60,40,15,56,105,120,100,60,21,84,168,
%T A103252 210,200,150,84,28,120,252,336,350,300,210,112,36,165,360,504,560,525,
%U A103252 420,280,144,45,220,495,720,840,840,735,560,360,180,55
%N A103252 Array A000292(n)*A000217(k), read by antidiagonals.
%H A103252 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.
%H A103252 Joaquín Figueroa, Ivan Gonzalez, and Daniel Salinas-Arizmendi, <a href="https://arxiv.org/abs/2503.23134">A Novel Transfer Matrix Framework for Multiple Dirac Delta Potentials</a>, arXiv:2503.23134 [quant-ph], 2025. See pp. 5, 9.
%F A103252 G.f.: x*y/((1 - x)^4*(1 - y)^3). - _Stefano Spezia_, May 21 2023
%e A103252 Array begins
%e A103252    1,   3,   6,  10,  15,  21,  28,   36,   45,   55, ...
%e A103252    4,  12,  24,  40,  60,  84, 112,  144,  180,  220, ...
%e A103252   10,  30,  60, 100, 150, 210, 280,  360,  450,  550, ...
%e A103252   20,  60, 120, 200, 300, 420, 560,  720,  900, 1100, ...
%e A103252   35, 105, 210, 350, 525, 735, 980, 1260, 1575, 1925, ...
%e A103252   ...
%t A103252 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 A103252 Cf. A000579 (antidiagonal sums).
%Y A103252 Main diagonal gives A004302.
%Y A103252 Cf. A000217, A000292.
%K A103252 nonn,tabl,easy
%O A103252 1,2
%A A103252 _Gary W. Adamson_, Mar 20 2005
%E A103252 More terms from _Stefano Spezia_, May 21 2023