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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

Table of n, a(n) for n=1..40.

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

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