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A174148
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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]}]]
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0
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1, 1, 1, 1, 12, 1, 1, 42, 42, 1, 1, 100, 360, 100, 1, 1, 195, 1700, 1700, 195, 1, 1, 336, 5775, 14000, 5775, 336, 1, 1, 532, 15876, 75950, 75950, 15876, 532, 1, 1, 792, 37632, 312816, 617400, 312816, 37632, 792, 1, 1, 1125, 79920, 1058400, 3630312, 3630312
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OFFSET
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0,5
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COMMENTS
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Row sums are:
1, 2, 14, 86, 562, 3792, 26224, 184718, 1319882, 9539516, 69594340,...
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LINKS
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FORMULA
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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]}]]
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EXAMPLE
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{1},
{1, 1},
{1, 12, 1},
{1, 42, 42, 1},
{1, 100, 360, 100, 1},
{1, 195, 1700, 1700, 195, 1},
{1, 336, 5775, 14000, 5775, 336, 1},
{1, 532, 15876, 75950, 75950, 15876, 532, 1},
{1, 792, 37632, 312816, 617400, 312816, 37632, 792, 1},
{1, 1125, 79920, 1058400, 3630312, 3630312, 1058400, 79920, 1125, 1},
{1, 1540, 155925, 3088800, 16881480, 29338848, 16881480, 3088800, 155925, 1540, 1}
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MATHEMATICA
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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]}]];
Table[Flatten[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 0, 10, 2}]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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