|
Search: id:A136454
|
|
|
| A136454 |
|
Triangle of coefficients of the Pollaczek polynomials with a=1, b=1 multiplied by n! to make then integers. |
|
+0
1
|
|
| 1, 2, 3, 2, 16, 15, -20, 10, 142, 105, -112, -736, -166, 1488, 945, 1376, -3504, -19788, -7250, 18258, 10395, 19552, 121280, -60228, -494944, -199484, 258144, 135135, -307648, 1418848, 6685320, -66308, -12424144, -5095512, 4142430, 2027025, -8279680, -49934080, 61100432, 307535872
(list; table; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
Row sums are:
{1, 5, 33, 237, 1419, -513, -220545, -3619989, 17673849,2456264493, 42178265649}
|
|
REFERENCES
|
Weisstein, Eric W. "Pollaczek Polynomial." http : // mathworld.wolfram.com/PollaczekPolynomial.html
|
|
FORMULA
|
a=1;b=1; P(x, n) = (1/n)*((2*n - 1 + 2*a)*x + 2*b)P(x, n - 1) - (n - 1)*P(x, n - 2)
|
|
EXAMPLE
|
{1},
{2, 3},
{2, 16, 15},
{-20, 10, 142, 105},
{-112, -736, -166, 1488, 945},
{1376, -3504, -19788, -7250,18258, 10395},
{19552, 121280, -60228, -494944, -199484, 258144, 135135},
{-307648, 1418848, 6685320, -66308, -12424144, -5095512, 4142430, 2027025},
{-8279680, -49934080, 61100432, 307535872, 52222204, -322593920, -131311764, 74475360, 34459425},
{160645888, -1074438528, -4677290976, 1814173360, 13103932920, 3282048948, -8777947688, -3513539196, 1483950690, 654729075},
{7027832576, 41671291392, -81409140960, -343698820096,22005521160, 543047764416, 157729661372, -251689021440, -98728555986, 32472422640, 13749310575}
|
|
MATHEMATICA
|
Clear[P, a, b] a = 1; b = 1; P[x, 0] = 1; P[x, 1] = (2*a + 1)*x + 2*b; P[x_, n_] := P[x, n] = (1/n)*((2*n - 1 + 2*a)*x + 2*b)P[x, n - 1] - (n - 1)*P[x, n - 2]; a0 = Table[CoefficientList[n!*P[x, n], x], {n, 0, 10}]; Flatten[a0]
|
|
CROSSREFS
|
Sequence in context: A164661 A104507 A101033 this_sequence A025522 A019228 A075121
Adjacent sequences: A136451 A136452 A136453 this_sequence A136455 A136456 A136457
|
|
KEYWORD
|
uned,tabl,sign
|
|
AUTHOR
|
Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 20 2008
|
|
|
Search completed in 0.002 seconds
|
