Search: id:A136448
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%I A136448
%S A136448 1,0,0,1,4,0,0,0,1,0,0,13,0,0,0,1,64,0,0,0,29,0,0,0,1,0,0,389,0,0,0,54,
               0,0,0,1,
%T A136448 2304,0,0,0,1433,0,0,0,90,0,0,0,1,0,0,21365,0,0,0,4079,0,0,0,139,0,0,0,
               1,147456,0,
%U A136448 0,0,113077,0,0,0,9839,0,0,0,203,0,0,0,1,0,0,1878021,0,0,0,443476,0,0,
               0,21098,0,0,0
%V A136448 1,0,0,1,-4,0,0,0,1,0,0,-13,0,0,0,1,64,0,0,0,-29,0,0,0,1,0,0,389,0,0,0,
               -54,0,0,0,1,
%W A136448 -2304,0,0,0,1433,0,0,0,-90,0,0,0,1,0,0,-21365,0,0,0,4079,0,0,0,-139,0,
               0,0,1,147456,0,
%X A136448 0,0,-113077,0,0,0,9839,0,0,0,-203,0,0,0,1,0,0,1878021,0,0,0,-443476,0,
               0,0,21098,0,0,0
%N A136448 A Hermite-like even powered polynomial recursion as a triangle of coefficients: 
               P(x, n) = x^2*P=(x, n - 1) - n^2*P(x, n - 2).
%C A136448 Roe Sums are:
%C A136448 {1, 1, -3, -12, 36, 336, -960, -17424, 44016, 1455360, -2946240};
%C A136448 The double functional integrals show this is nonorthogonal polynomials 
               set:
%C A136448 Table[Table[Integrate[Exp[ -x^2/2]*P[x, n]*P[x, m], {x, -Infinity, Infinity}], 
               {n, 0, 10}], {m, 0, 10}]
%C A136448 for the Hermite weight function on an Infinite domain.
%F A136448 P(x,0)=1;P(x,2)=x^2 P(x, n) = x^2*P=(x, n - 1) - n^2*P(x, n - 2)
%e A136448 {1},
%e A136448 {0, 0, 1},
%e A136448 {-4, 0, 0, 0, 1},
%e A136448 {0, 0, -13, 0, 0, 0, 1},
%e A136448 {64, 0, 0, 0, -29, 0, 0, 0, 1},
%e A136448 {0, 0, 389, 0, 0, 0, -54, 0, 0, 0, 1},
%e A136448 {-2304, 0, 0, 0,1433, 0, 0, 0, -90, 0, 0, 0, 1},
%e A136448 {0, 0, -21365, 0, 0, 0, 4079, 0, 0, 0, -139, 0, 0, 0, 1},
%e A136448 {147456, 0, 0, 0, -113077, 0, 0, 0, 9839, 0, 0, 0, -203, 0, 0, 0, 1},
%e A136448 {0, 0, 1878021, 0, 0, 0, -443476, 0, 0, 0, 21098, 0, 0, 0, -284,0, 0, 
               0, 1},
%e A136448 {-14745600, 0, 0, 0, 13185721, 0, 0, 0, -1427376, 0,0, 0, 41398, 0, 0, 
               0, -384, 0, 0, 0, 1}
%t A136448 P[x, 0] = 1; P[x, 1] = x^2; P[x_, n_] := P[x, n] = x^2*P[x, n - 1] - 
               n^2*P[x, n - 2]; Table[ExpandAll[P[x, n]], {n, 0, 10}]; a = Table[CoefficientList[P[x, 
               n], x], {n, 0, 10}]; Flatten[a]
%Y A136448 Sequence in context: A108708 A005925 A070206 this_sequence A128975 A152894 
               A152898
%Y A136448 Adjacent sequences: A136445 A136446 A136447 this_sequence A136449 A136450 
               A136451
%K A136448 uned,tabl,sign
%O A136448 1,5
%A A136448 Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 19 2008

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