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 A176422 A symmetrical triangle sequence;q=4;c(n,q)=Product[1 - q^i, {i, 1, n}];t(n,m,q)=1 c(n, q)/(c[m, q)*c(n - m, q))-Binomial[n, m] 0
 1, 1, 1, 1, 4, 1, 1, 19, 19, 1, 1, 82, 352, 82, 1, 1, 337, 5788, 5788, 337, 1, 1, 1360, 93079, 376786, 93079, 1360, 1, 1, 5455, 1490833, 24208579, 24208579, 1490833, 5455, 1, 1, 21838, 23859082, 1550842030, 6221613472, 1550842030, 23859082, 21838, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Row sums are: {1, 2, 6, 40, 518, 12252, 565666, 51409736, 9371059374, 3387887031700, 2463333456291194,...}. LINKS Table of n, a(n) for n=0..45. FORMULA q=4; c(n,q)=Product[1 - q^i, {i, 1, n}]; t(n,m,q)=t(n,m,q)=1 c(n, q)/(c[m, q)*c(n - m, q))-Binomial[n, m] EXAMPLE {1}, {1, 1}, {1, 4, 1}, {1, 19, 19, 1}, {1, 82, 352, 82, 1}, {1, 337, 5788, 5788, 337, 1}, {1, 1360, 93079, 376786, 93079, 1360, 1}, {1, 5455, 1490833, 24208579, 24208579, 1490833, 5455, 1}, {1, 21838, 23859082, 1550842030, 6221613472, 1550842030, 23859082, 21838, 1}, {1, 87373, 381767554, 99277752466, 1594283908456, 1594283908456, 99277752466, 381767554, 87373, 1}, {1, 349516, 6108368761, 6354157930606, 408235958349076, 1634141006295274, 408235958349076, 6354157930606, 6108368761, 349516, 1} MATHEMATICA c[n_, q_] = Product[1 - q^i, {i, 1, n}]; t[n_, m_, q_] = c[n, q]/(c[m, q]*c[n - m, q]) - Binomial[n, m] + 1; Table[Flatten[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 2, 12}] CROSSREFS Sequence in context: A323849 A254442 A340476 * A156586 A181544 A154283 Adjacent sequences: A176419 A176420 A176421 * A176423 A176424 A176425 KEYWORD nonn,tabl,uned AUTHOR Roger L. Bagula, Apr 17 2010 STATUS approved

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Last modified May 27 17:52 EDT 2024. Contains 372880 sequences. (Running on oeis4.)