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A158868
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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}].
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0
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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
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OFFSET
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1,2
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COMMENTS
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Row sums are:
{1, 7, 27, 258, 1407, 18426, 133560, 2249640, 20523780, 424652760,...}.
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LINKS
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Table of n, a(n) for n=1..40.
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FORMULA
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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}].
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EXAMPLE
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{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}
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MATHEMATICA
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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[%]
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CROSSREFS
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Sequence in context: A277710 A286148 A194048 * A104634 A194008 A060422
Adjacent sequences: A158865 A158866 A158867 * A158869 A158870 A158871
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KEYWORD
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nonn,tabl,uned
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AUTHOR
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Roger L. Bagula, Mar 28 2009
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STATUS
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approved
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