The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

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