|
Search: id:A158868
|
|
|
| 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
|
|
| 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; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
Row sums are:
{1, 7, 27, 258, 1407, 18426, 133560, 2249640, 20523780, 424652760,...}.
|
|
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: A082153 A013946 A085436 this_sequence A104634 A060422 A128142
Adjacent sequences: A158865 A158866 A158867 this_sequence A158869 A158870 A158871
|
|
KEYWORD
|
nonn,tabl,uned
|
|
AUTHOR
|
Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 28 2009
|
|
|
Search completed in 0.002 seconds
|
