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A158867
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A polynomial integration sequence: t(n,m)=((2*n + 1)!!/(4*2^(Floor[( n - 1)/2])))Integrate[(1 - x)^(Floor[(n - 1)/2] + Floor[m/2] + 1)*(1 + x)^(Floor[(m - 1)/2] + Floor[n/2] + 1), {x, -1, 1}].
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1, 5, 4, 14, 14, 12, 126, 108, 108, 96, 594, 594, 528, 528, 480, 7722, 6864, 6864, 6240, 6240, 5760, 51480, 51480, 46800, 46800, 43200, 43200, 40320, 875160, 795600, 795600, 734400, 734400, 685440, 685440, 645120, 7558200, 7558200, 6976800
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Row sums are:
{1, 9, 40, 438, 2724, 39690, 323280, 5951160, 60156720, 1342618200,...}.
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FORMULA
| t(n,m)=((2*n + 1)!!/(4*2^(Floor[( n - 1)/2])))Integrate[(1 - x)^(Floor[(n - 1)/2] + Floor[m/2] + 1)*(1 + x)^(Floor[(m - 1)/2] + Floor[n/2] + 1), {x, -1, 1}].
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EXAMPLE
| {1},
{5, 4},
{14, 14, 12},
{126, 108, 108, 96},
{594, 594, 528, 528, 480},
{7722, 6864, 6864, 6240, 6240, 5760},
{51480, 51480, 46800, 46800, 43200, 43200, 40320},
{875160, 795600, 795600, 734400, 734400, 685440, 685440, 645120},
{7558200, 7558200, 6976800, 6976800, 6511680, 6511680, 6128640, 6128640, 5806080},
{158722200, 146512800, 146512800, 136745280, 136745280, 128701440, 128701440, 121927680, 121927680, 116121600}
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MATHEMATICA
| Clear[t, n, m] t[n_, m_] = ((2*n + 1)!!/( 4*2^(Floor[(n - 1)/2])))Integrate[(1 - x)^(Floor[(n - 1)/2] + Floor[m/2] + 1)*(1 + x)^(Floor[(m - 1)/2] + Floor[n/2] + 1), {x, -1, 1}];
a = Table[t[n, m], {n, 10}, {m, 1, n}];
Flatten[%]
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CROSSREFS
| Sequence in context: A147685 A078930 A094414 * A107984 A133178 A154225
Adjacent sequences: A158864 A158865 A158866 * A158868 A158869 A158870
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KEYWORD
| nonn,tabl,uned
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 28 2009
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