|
Search: id:A137320
|
|
|
| A137320 |
|
A triangular sequence from a coefficients of a raising factorial polynomial sequence recursion: p(x, n) = (m*x + n - 1)*p(x, n - 1). |
|
+0
2
|
|
| 1, 0, 2, 0, 2, 4, 0, 4, 12, 8, 0, 12, 44, 48, 16, 0, 48, 200, 280, 160, 32, 0, 240, 1096, 1800, 1360, 480, 64, 0, 1440, 7056, 12992, 11760, 5600, 1344, 128, 0, 10080, 52272, 105056, 108304, 62720, 20608, 3584, 256, 0, 80640, 438336, 944992, 1076544, 718368
(list; table; graph; listen)
|
|
|
OFFSET
|
1,3
|
|
|
COMMENT
|
Row sums are factorials.
|
|
REFERENCES
|
Steve Roman, The Umbral Calculus, Dover Publications, New York (1984), pp. 62-63
|
|
FORMULA
|
p(x, n) = (m*x + n - 1)*p(x, n - 1).
|
|
EXAMPLE
|
{1},
{0, 2},
{0, 2, 4},
{0, 4, 12, 8},
{0, 12, 44, 48, 16},
{0, 48, 200, 280, 160, 32},
{0, 240, 1096, 1800, 1360, 480, 64},
{0, 1440, 7056, 12992, 11760,5600, 1344, 128},
{0, 10080, 52272, 105056, 108304, 62720, 20608, 3584, 256},
{0, 80640, 438336, 944992, 1076544, 718368, 290304, 69888, 9216, 512},
{0, 725760, 4106304, 9381600, 11578880, 8618400, 4049472, 1209600, 222720, 23040, 1024}
|
|
MATHEMATICA
|
m = 2; p[x, 0] = 1; p[x, -1] = 0; p[x, 1] = m*x; p[x_, n_] := p[x, n] = (m*x + n - 1)*p[x, n - 1]; Table[ExpandAll[p[x, n]], {n, 0, 10}]; a = Table[CoefficientList[p[x, n], x], {n, 0, 10}]
|
|
CROSSREFS
|
Apart from signs, same as A137312.
Adjacent sequences: A137317 A137318 A137319 this_sequence A137321 A137322 A137323
Sequence in context: A126440 A131186 A137312 this_sequence A071961 A120557 A092594
|
|
KEYWORD
|
nonn,uned,tabl
|
|
AUTHOR
|
Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 20 2008
|
|
|
Search completed in 0.002 seconds
|
