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 A158868 A polynomial integration sequence: t(n,m)=((2*n + 1)!!/(2^(Floor[(n - 1)/ 2] + Floor[m/2] + 1)))Integrate[(2 - 2*x)^(Floor[(n - 1)/2] + Floor[m/2] + 1)*(2*x)^(Floor[(m - 1)/2] + Floor[n/2] + 1), {x, 0, 1}]. 0
 1, 5, 2, 14, 7, 6, 126, 54, 54, 24, 594, 297, 264, 132, 120, 7722, 3432, 3432, 1560, 1560, 720, 51480, 25740, 23400, 11700, 10800, 5400, 5040, 875160, 397800, 397800, 183600, 183600, 85680, 85680, 40320, 7558200, 3779100, 3488400, 1744200 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Row sums are: {1, 7, 27, 258, 1407, 18426, 133560, 2249640, 20523780, 424652760,...}. LINKS FORMULA t(n,m)=((2*n + 1)!!/(2^(Floor[(n - 1)/ 2] + Floor[m/2] + 1)))Integrate[(2 - 2*x)^(Floor[(n - 1)/2] + Floor[m/2] + 1)*(2*x)^(Floor[(m - 1)/2] + Floor[n/2] + 1), {x, 0, 1}]. EXAMPLE {1}, {5, 2}, {14, 7, 6}, {126, 54, 54, 24}, {594, 297, 264, 132, 120}, {7722, 3432, 3432, 1560, 1560, 720}, {51480, 25740, 23400, 11700, 10800, 5400, 5040}, {875160, 397800, 397800, 183600, 183600, 85680, 85680, 40320}, {7558200, 3779100, 3488400, 1744200, 1627920, 813960, 766080, 383040, 362880}, {158722200, 73256400, 73256400, 34186320, 34186320, 16087680, 16087680, 7620480, 7620480, 3628800} MATHEMATICA Clear[t, n, m] t[n_, m_] = ((2*n + 1)!!/(2^(Floor[(n - 1)/ 2] + Floor[m/2] + 1)))Integrate[(2 - 2*x)^(Floor[(n - 1)/2] + Floor[m/2] + 1)*(2*x)^(Floor[(m - 1)/2] + Floor[n/2] + 1), {x, 0, 1}]; a = Table[t[n, m], {n, 10}, {m, 1, n}]; Flatten[%] CROSSREFS Sequence in context: A277710 A286148 A194048 * A104634 A194008 A060422 Adjacent sequences:  A158865 A158866 A158867 * A158869 A158870 A158871 KEYWORD nonn,tabl,uned AUTHOR Roger L. Bagula, Mar 28 2009 STATUS approved

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Last modified June 17 17:46 EDT 2021. Contains 345085 sequences. (Running on oeis4.)