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A129367 Triangle T(n, k) = A002415(n-k+3)*A002415(k+3), read by rows.

%I A129367 #15 Feb 01 2024 01:50:33
%S A129367 36,120,120,300,400,300,630,1000,1000,630,1176,2100,2500,2100,1176,
%T A129367 2016,3920,5250,5250,3920,2016,3240,6720,9800,11025,9800,6720,3240,
%U A129367 4950,10800,16800,20580,20580,16800,10800,4950,7260,16500,27000,35280,38416,35280,27000,16500,7260
%N A129367 Triangle T(n, k) = A002415(n-k+3)*A002415(k+3), read by rows.
%H A129367 G. C. Greubel, <a href="/A129367/b129367.txt">Rows n = 0..50 of the triangle, flattened</a>
%F A129367 T(n,k) = A002415(n-k+3)*A002415(k+3), where A002415(n) = n^2*(n^2-1)/12.
%F A129367 T(n, n-k) = T(n, k).
%e A129367 Triangle begins as:
%e A129367     36;
%e A129367    120,   120;
%e A129367    300,   400,   300;
%e A129367    630,  1000,  1000,   630;
%e A129367   1176,  2100,  2500,  2100,  1176;
%e A129367   2016,  3920,  5250,  5250,  3920,  2016;
%e A129367   3240,  6720,  9800, 11025,  9800,  6720,  3240;
%e A129367   4950, 10800, 16800, 20580, 20580, 16800, 10800,  4950;
%e A129367   7260, 16500, 27000, 35280, 38416, 35280, 27000, 16500, 7260;
%t A129367 A129367[n_, k_]:= Binomial[(n-k+3)^2, 2]*Binomial[(k+3)^2, 2]/36;
%t A129367 Table[A129367[n,k], {n,0,12}, {k,0,n}]//Flatten
%o A129367 (Magma) [Binomial((n-k+3)^2,2)*Binomial((k+3)^2,2)/36: k in [0..n], n in [0..12]]; // _G. C. Greubel_, Jan 31 2024
%o A129367 (SageMath)
%o A129367 def A129367(n,k): return binomial((n-k+3)^2,2)*binomial((k+3)^2,2)/36
%o A129367 flatten([[A129367(n,k) for k in range(n+1)] for n in range(13)]) # _G. C. Greubel_, Jan 31 2024
%Y A129367 Cf. A002415, A117662.
%K A129367 nonn,tabl,easy,less
%O A129367 0,1
%A A129367 _Roger L. Bagula_ and _Gary W. Adamson_, Aug 25 2008
%E A129367 Edited by _G. C. Greubel_, Jan 31 2024