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A158867 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}]. 0
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; text; internal format)
OFFSET

1,2

COMMENTS

Row sums are:

{1, 9, 40, 438, 2724, 39690, 323280, 5951160, 60156720, 1342618200,...}.

LINKS

Table of n, a(n) for n=1..39.

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}].

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}

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[%]

CROSSREFS

Sequence in context: A329162 A344817 A094414 * A107984 A133178 A154225

Adjacent sequences:  A158864 A158865 A158866 * A158868 A158869 A158870

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Mar 28 2009

STATUS

approved

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Last modified June 16 21:55 EDT 2021. Contains 345080 sequences. (Running on oeis4.)