|
%I #3 Mar 30 2012 17:34:26
%S 1,0,-2,-3,0,3,-12,14,2,-4,-57,90,-28,-10,5,-384,666,-306,0,30,-6,
%T -3441,6342,-3419,368,213,-70,7,-38220,74202,-44886,7834,1886,-948,
%U 140,-8,-504111,1023780,-679176,155604,15918,-14652,2880,-252,9,-7683576,16226262,-11611074,3201728,55680,-243876,61670
%N 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 Row sums are: {1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0}
%F 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 {1},
%e {0, -2},
%e {-3,0, 3},
%e {-12, 14, 2, -4},
%e {-57, 90, -28, -10, 5},
%e {-384, 666, -306, 0,30, -6},
%e {-3441, 6342, -3419,368, 213, -70, 7},
%e {-38220, 74202, -44886, 7834, 1886, -948, 140, -8},
%e {-504111, 1023780, -679176, 155604, 15918, -14652, 2880, -252, 9},
%e {-7683576, 16226262, -11611074, 3201728, 55680, -243876, 61670, -7224, 420, -10},
%e {-132759147, 290128956, -221191449, 69967716, -3029890, -4304544, 1374390, -201388, 16005, -660, 11}
%t 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]
%K tabl,sign
%O 1,3
%A _Roger L. Bagula_, Apr 27 2008
|
