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

 

Logo


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

Table of n, a(n) for n=1..40.

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

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 3 04:26 EST 2021. Contains 341756 sequences. (Running on oeis4.)