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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
 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Row sums are: 1, 2, 14, 86, 562, 3792, 26224, 184718, 1319882, 9539516, 69594340,... LINKS FORMULA 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]}]] EXAMPLE {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} MATHEMATICA 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}] CROSSREFS Sequence in context: A186432 A176489 A174039 * A155495 A157273 A168518 Adjacent sequences:  A174145 A174146 A174147 * A174149 A174150 A174151 KEYWORD nonn,tabl,uned AUTHOR Roger L. Bagula, Mar 09 2010 STATUS approved

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Last modified September 23 18:51 EDT 2020. Contains 337315 sequences. (Running on oeis4.)