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A174148 A symmetrical binomial product triangle sequence:q=2; 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]}]] 0

%I #2 Mar 30 2012 17:34:39

%S 1,1,1,1,12,1,1,42,42,1,1,100,360,100,1,1,195,1700,1700,195,1,1,336,

%T 5775,14000,5775,336,1,1,532,15876,75950,75950,15876,532,1,1,792,

%U 37632,312816,617400,312816,37632,792,1,1,1125,79920,1058400,3630312,3630312

%N A symmetrical binomial product triangle sequence:q=2; 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, 14, 86, 562, 3792, 26224, 184718, 1319882, 9539516, 69594340,...

%F q=2;

%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, 12, 1},

%e {1, 42, 42, 1},

%e {1, 100, 360, 100, 1},

%e {1, 195, 1700, 1700, 195, 1},

%e {1, 336, 5775, 14000, 5775, 336, 1},

%e {1, 532, 15876, 75950, 75950, 15876, 532, 1},

%e {1, 792, 37632, 312816, 617400, 312816, 37632, 792, 1},

%e {1, 1125, 79920, 1058400, 3630312, 3630312, 1058400, 79920, 1125, 1},

%e {1, 1540, 155925, 3088800, 16881480, 29338848, 16881480, 3088800, 155925, 1540, 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 0,5

%A _Roger L. Bagula_, Mar 09 2010

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Last modified March 28 08:22 EDT 2024. Contains 371236 sequences. (Running on oeis4.)