%I #2 Mar 30 2012 17:34:39
%S 1,1,1,1,0,1,1,120,120,1,1,720,5400,720,1,1,2520,84700,84700,2520,1,1,
%T 6720,712950,3136000,712950,6720,1,1,15120,4064256,56080500,56080500,
%U 4064256,15120,1,1,30240,17745840,619178112,1944810000,619178112
%N A symmetrical binomial product triangle sequence:q=4; t(n,m,q)=If[n == 0 || n == 1, 1, Product[Binomial[n + i, m + i], {i, -Floor[q/2], Floor[q/2]}] + Product[Binomial[n + i, n - m + i], {i, -Floor[q/2], Floor[q/2]}]]
%C Row sums are:
%C 1, 2, 2, 242, 6842, 174442, 4575342, 120319754, 3218718386, 87130425890,
%C 2387489480048,...
%F q=4;
%F t(n,m,q)=If[n == 0 || n == 1, 1, Product[Binomial[n + i, m + i], {i, -Floor[q/2], Floor[q/2]}] +
%F Product[Binomial[n + i, n - m + i], {i, -Floor[q/2], Floor[q/2]}]]
%e {1},
%e {1, 1},
%e {1, 0, 1},
%e {1, 120, 120, 1},
%e {1, 720, 5400, 720, 1},
%e {1, 2520, 84700, 84700, 2520, 1},
%e {1, 6720, 712950, 3136000, 712950, 6720, 1},
%e {1, 15120, 4064256, 56080500, 56080500, 4064256, 15120, 1},
%e {1, 30240, 17745840, 619178112, 1944810000, 619178112, 17745840, 30240, 1},
%e {1, 55440, 63795600, 4857209280, 38644152624, 38644152624, 4857209280, 63795600, 55440, 1},
%e {1, 95040, 197735175, 29523225600, 513405390960, 1301236586496, 513405390960, 29523225600, 197735175, 95040, 1}
%t t[n_, m_, q_] = If[n == 0 || n == 1, 1, Product[Binomial[n + i, m + i], {i, - Floor[q/2], Floor[q/2]}] + Product[Binomial[n + i, n - m + i], { i, -Floor[q/2], Floor[q/2]}]];
%t Table[Flatten[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 0, 10, 2}]
%K nonn,tabl,uned
%O 0,8
%A _Roger L. Bagula_, Mar 09 2010
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