Search: id:A136532
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%I A136532
%S A136532 1,0,3,8,16,4,60,65,50,5,384,168,462,108,6,2380,763,3836,1624,196,7,14208,
%T A136532 21248,29560,21472,4256,320,8,73836,302571,199998,269127,78840,9387,486,
               9,
%U A136532 176000,3761240,854530,3288940,1360150,228880,18430,700,10,3824964,44711623
%V A136532 1,0,-3,-8,-16,4,-60,-65,50,-5,-384,-168,462,-108,6,-2380,763,3836,-1624,
               196,-7,-14208,
%W A136532 21248,29560,-21472,4256,-320,8,-73836,302571,199998,-269127,78840,-9387,
               486,-9,
%X A136532 -176000,3761240,854530,-3288940,1360150,-228880,18430,-700,10,3824964,
               44711623
%N A136532 Coefficients of Laguerre recursive polynomials with an (n+2)!/2 multiplication 
               factor and alpha=a0 =-1 from Hochstadt: P(x, n) = (2*n + a0 + 1 - 
               x)*P(x, n - 1)/(n + 1) - n*P(x, n - 2)/(n + 1);.
%C A136532 Table[Apply[Plus, CoefficientList[(n + 2)!P[x, n]/2, x]], {n, 0, 10}];
%C A136532 Row sums:
%C A136532 {1, -3, -20, -80, -192, 784, 19072, 229536, 2299840, 20282944, 144429312}
%D A136532 page 8 and page 42 - 43; Harry Hochstadt, The Functions of Mathematical 
               Physics, Dover, New York, 1986
%F A136532 a0=-1; 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 A136532 {1},
%e A136532 {0, -3},
%e A136532 {-8, -16, 4},
%e A136532 {-60, -65,50, -5},
%e A136532 {-384, -168, 462, -108, 6},
%e A136532 {-2380, 763, 3836, -1624, 196, -7},
%e A136532 {-14208, 21248, 29560, -21472, 4256, -320, 8},
%e A136532 {-73836, 302571, 199998, -269127, 78840, -9387, 486, -9},
%e A136532 {-176000, 3761240, 854530, -3288940, 1360150, -228880, 18430, -700, 10},
%e A136532 {3824964, 44711623, -7017472, -39417422, 22743644, -5098676, 568568, 
               -33242,968, -11},
%e A136532 {104573760, 520004832, -304428396, -457688256,376007784, -108589488, 
               15755712, -1261536, 56184, -1296, 12}
%t A136532 a0 = -1; 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 A136532 Cf. A021009.
%Y A136532 Sequence in context: A065500 A120341 A094357 this_sequence A030417 A123979 
               A013583
%Y A136532 Adjacent sequences: A136529 A136530 A136531 this_sequence A136533 A136534 
               A136535
%K A136532 uned,tabl,sign
%O A136532 1,3
%A A136532 Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 23 2008

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