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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
OFFSET
1,2
LINKS
Eric Weisstein's World of Mathematics, Pollaczek Polynomial.
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},...
MATHEMATICA
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 A350622 A019228
KEYWORD
uned,tabl,sign
AUTHOR
Roger L. Bagula, Mar 20 2008
STATUS
approved