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 A176427 A symmetrical triangle sequence:q=2;c(n,q)=Product[1 - q^i, {i, 1, n}];t(n,m,q)=-Eulerian[n + 1, m] + 2*c(n, q)/(c(m, q)*c(n - m, q)) 0
 1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 4, 4, 1, 1, 5, 8, 8, 5, 1, 1, 6, 111, 374, 111, 6, 1, 1, 7, 1041, 8003, 8003, 1041, 7, 1, 1, 8, 6982, 106076, 245384, 106076, 6982, 8, 1, 1, 9, 39030, 1120878, 5309140, 5309140, 1120878, 39030, 9, 1, 1, 10, 195865, 10491942 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Row sums are: {1, 2, 4, 8, 14, 28, 610, 18104, 471518, 12938116, 419594410,...}. LINKS FORMULA q=2; c(n,q)=Product[1 - q^i, {i, 1, n}]; t(n,m,q)=-Eulerian[n + 1, m] + 2*c(n, q)/(c(m, q)*c(n - m, q)) EXAMPLE {1}, {1, 1}, {1, 2, 1}, {1, 3, 3, 1}, {1, 4, 4, 4, 1}, {1, 5, 8, 8, 5, 1}, {1, 6, 111, 374, 111, 6, 1}, {1, 7, 1041, 8003, 8003, 1041, 7, 1}, {1, 8, 6982, 106076, 245384, 106076, 6982, 8, 1}, {1, 9, 39030, 1120878, 5309140, 5309140, 1120878, 39030, 9, 1}, {1, 10, 195865, 10491942, 97749860, 202719054, 97749860, 10491942, 195865, 10, 1} MATHEMATICA << DiscreteMath`Combinatorica` ; c[n_, q_] = Product[1 - q^i, {i, 1, n}]; t[n_, m_, q_] = -Eulerian[n + 1, m] + 2*c[n, q]/(c[m, q]*c[n - m, q]); Table[Flatten[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 2, 12}] CROSSREFS Sequence in context: A318274 A049695 A096589 * A099573 A107430 A255741 Adjacent sequences:  A176424 A176425 A176426 * A176428 A176429 A176430 KEYWORD nonn,tabl,uned AUTHOR Roger L. Bagula, Apr 17 2010 STATUS approved

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Last modified August 20 03:33 EDT 2019. Contains 326139 sequences. (Running on oeis4.)