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%I #4 Mar 30 2012 17:34:23
%S 1,3,-3,12,-24,4,60,-180,65,-5,360,-1440,822,-132,6,2520,-12600,9954,
%T -2478,231,-7,20160,-120960,122832,-41856,5976,-368,8,181440,-1270080,
%U 1581768,-688392,133380,-12492,549,-9,1814400,-14515200,21462480,-11412000,2806200,-354720,23610,-780,10,19958400
%N Coefficients of Laguerre recursive polynomials with an (n+2)!/2 multiplication factor and alpha=a0 =0 from Hochstadt: P(x, n) = (2*n + a0 + 1 - x)*P(x, n - 1)/(n + 1) - n*P(x, n - 2)/(n + 1);.
%C Table[Apply[Plus, CoefficientList[(n + 2)!P[x, n]/2, x]], {n, 0, 10}];
%C Row sums:
%C {1, 0, -8, -60, -384, -2380, -14208, -73836, -176000, 3824964, 104573760}
%D page 8 and page 42 - 43; Harry Hochstadt, The Functions of Mathematical Physics, Dover, New York, 1986
%F a0=0; p(x,0)=1;p(x,1)=1+a0-x; P(x, n) = (2*n + a0 + 1 - x)*P(x, n - 1)/(n + 1) - n*P(x, n - 2)/(n + 1);
%e {1},
%e {3, -3},
%e {12, -24, 4},
%e {60, -180,65, -5},
%e {360, -1440, 822, -132, 6},
%e {2520, -12600, 9954, -2478, 231, -7},
%e {20160, -120960,122832, -41856, 5976, -368, 8},
%e {181440, -1270080, 1581768, -688392, 133380, -12492, 549, -9},
%e {1814400, -14515200, 21462480, -11412000, 2806200, -354720, 23610, -780, 10}, {19958400, -179625600, 307937520, -193968720, 57998160, -9263760, 829290, -41382, 1067, -11},
%e {239500800, -2395008000, 4675026240, -3410138880, 1203543360, -232928640, 26271000, -1759104, 68388, -1416, 12}
%t a0 = 0; P[x, 0] = 1; P[x, 1] = 1 + a0 - x; P[x_, n_] := P[x, n] = (2*n + a0 + 1 - x)*P[x, n - 1]/(n + 1) - n*P[x, n - 2]/(n + 1); Table[ExpandAll[(n + 2)!*P[x, n]/2], {n, 0, 10}]; a = Table[CoefficientList[(n + 2)!*P[x, n]/2, x], {n, 0, 10}]; Flatten[a]
%Y Cf. A021009.
%K uned,tabl,sign
%O 1,2
%A _Roger L. Bagula_, Mar 23 2008
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