%I A137663
%S A137663 1,0,2,3,0,3,12,14,2,4,57,90,28,10,5,384,666,306,0,30,6,3441,6342,3419,
               368,
%T A137663 213,70,7,38220,74202,44886,7834,1886,948,140,8,504111,1023780,679176,
               155604,
%U A137663 15918,14652,2880,252,9,7683576,16226262,11611074,3201728,55680,243876,
               61670
%V A137663 1,0,-2,-3,0,3,-12,14,2,-4,-57,90,-28,-10,5,-384,666,-306,0,30,-6,-3441,
               6342,-3419,368,
%W A137663 213,-70,7,-38220,74202,-44886,7834,1886,-948,140,-8,-504111,1023780,-679176,
               155604,
%X A137663 15918,-14652,2880,-252,9,-7683576,16226262,-11611074,3201728,55680,-243876,
               61670
%N A137663 Triangular sequence of coefficients from a polynomial recursion: p(x,
               n)=-2 (-(n - 1) + x)*p(x, n - 1) + (-(n + 1) + (n + 2)* x - x^2)p(x, 
               n - 2).
%C A137663 Row sums are: {1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0}
%F A137663 p(x,n)=-2 (-(n - 1) + x)*p[x, n - 1] + (-(n + 1) + (n + 2)* x - x^2)p[x, 
               n - 2]; out_n,m=Coefficients(p(x,n)
%e A137663 {1},
%e A137663 {0, -2},
%e A137663 {-3,0, 3},
%e A137663 {-12, 14, 2, -4},
%e A137663 {-57, 90, -28, -10, 5},
%e A137663 {-384, 666, -306, 0,30, -6},
%e A137663 {-3441, 6342, -3419,368, 213, -70, 7},
%e A137663 {-38220, 74202, -44886, 7834, 1886, -948, 140, -8},
%e A137663 {-504111, 1023780, -679176, 155604, 15918, -14652, 2880, -252, 9},
%e A137663 {-7683576, 16226262, -11611074, 3201728, 55680, -243876, 61670, -7224, 
               420, -10},
%e A137663 {-132759147, 290128956, -221191449, 69967716, -3029890, -4304544, 1374390, 
               -201388, 16005, -660, 11}
%t A137663 Clear[p, x] p[x, 0] = 1; p[x, -1] = 0; p[x_, n_] := p[x, n] = -2 (-(n 
               - 1) + x)*p[x, n - 1] + (-(n + 1) + (n + 2)* x - x^2)p[x, n - 2]; 
               g = Table[ExpandAll[p[x, n]], {n, 0, 10}]; a = Table[ CoefficientList[p[x, 
               n], x], {n, 0, 10}]; Flatten[a]
%Y A137663 Sequence in context: A079777 A047773 A035549 this_sequence A161628 A122059 
               A164917
%Y A137663 Adjacent sequences: A137660 A137661 A137662 this_sequence A137664 A137665 
               A137666
%K A137663 tabl,sign
%O A137663 1,3
%A A137663 Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 27 2008