|
Search: id:A137376
|
|
|
| A137376 |
|
Triangular sequence from coefficients of Meixner polynomials from expansion of: p(x)=(1 - t/c)*(1 - t)^(-x - b);c = 1/2; b = 1;. |
|
+0
1
|
|
| 1, -1, 1, -2, -1, 1, -6, -7, 0, 1, -24, -38, -13, 2, 1, -120, -226, -125, -15, 5, 1, -720, -1524, -1076, -285, -5, 9, 1, -5040, -11628, -9604, -3521, -490, 28, 14, 1, -40320, -99504, -91988, -41020, -8911, -616, 98, 20, 1, -362880, -945936, -953532, -487432, -134757, -18375, -378, 222, 27, 1, -3628800
(list; table; graph; listen)
|
|
|
OFFSET
|
1,4
|
|
|
COMMENT
|
Row sums are: {1, 0, -2, -12, -72, -480, -3600, -30240, -282240, -2903040, -32659200}
|
|
REFERENCES
|
Weisstein, Eric W. "Meixner Polynomial of the First Kind. " http://mathworld.wolfram.com/MeixnerPolynomialoftheFirstKind.html
|
|
FORMULA
|
p(x)=(1 - t/c)*(1 - t)^(-x - b);c = 1/2; b = 1;-> M(x,n) out(n,m)Coefficients(n!M(x,n))
|
|
EXAMPLE
|
{1},
{-1, 1},
{-2, -1, 1},
{-6, -7, 0, 1},
{-24, -38, -13, 2, 1},
{-120, -226, -125, -15, 5, 1},
{-720, -1524, -1076, -285, -5, 9, 1},
{-5040, -11628, -9604, -3521, -490,28, 14, 1},
{-40320, -99504, -91988, -41020, -8911, -616, 98, 20,1},
{-362880, -945936, -953532, -487432, -134757, -18375, -378,222, 27, 1},
{-3628800, -9902880, -10700424, -6064100, -1969570, -363405, -31227, 750, 420, 35, 1}
|
|
MATHEMATICA
|
Clear[p, x, t, c, b] c = 1/2; b = 1; p[t_] = (1 - t/c)*(1 - t)^(-x - b); Table[ ExpandAll[n!*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n]], {n, 0, 10}]; a = Table[ CoefficientList[n!*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n], x], {n, 0, 10}]; Flatten[a]
|
|
CROSSREFS
|
Cf. A000587.
Adjacent sequences: A137373 A137374 A137375 this_sequence A137377 A137378 A137379
Sequence in context: A145903 A009963 A008300 this_sequence A039761 A144089 A039763
|
|
KEYWORD
|
uned,tabl,sign
|
|
AUTHOR
|
Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 09 2008
|
|
|
Search completed in 0.002 seconds
|
