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%I #12 Feb 12 2024 08:20:54
%S 1,2,3,2,16,15,-20,10,142,105,-112,-736,-166,1488,945,1376,-3504,
%T -19788,-7250,18258,10395,19552,121280,-60228,-494944,-199484,258144,
%U 135135,-307648,1418848,6685320,-66308,-12424144,-5095512,4142430,2027025,-8279680,-49934080,61100432,307535872
%N Triangle of coefficients of the Pollaczek polynomials with a=1, b=1 multiplied by n! to make then integers.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PollaczekPolynomial.html">Pollaczek Polynomial</a>.
%e {1},
%e {2, 3},
%e {2, 16, 15},
%e {-20, 10, 142, 105},
%e {-112, -736, -166, 1488, 945},
%e {1376, -3504, -19788, -7250,18258, 10395},
%e {19552, 121280, -60228, -494944, -199484, 258144, 135135},
%e {-307648, 1418848, 6685320, -66308, -12424144, -5095512, 4142430, 2027025},...
%t a = 1; b = 1;
%t P[x, 0] = 1;
%t P[x, 1] = (2*a + 1)*x + 2*b;
%t 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];
%t a0 = Table[CoefficientList[n!*P[x, n], x], {n, 0, 10}];
%t Flatten[a0]
%K uned,tabl,sign
%O 1,2
%A _Roger L. Bagula_, Mar 20 2008
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