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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A136454 Triangle of coefficients of the Pollaczek polynomials with a=1, b=1 multiplied by n! to make then integers. 0
 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; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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 LINKS 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 * A025522 A019228 A332734 Adjacent sequences:  A136451 A136452 A136453 * A136455 A136456 A136457 KEYWORD uned,tabl,sign AUTHOR Roger L. Bagula, Mar 20 2008 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.

Last modified September 18 13:54 EDT 2021. Contains 347527 sequences. (Running on oeis4.)