%I #3 Mar 30 2012 17:34:26
%S 1,8,3,24,48,9,-192,216,216,27,-2976,-2304,1296,864,81,-57600,-44640,
%T -17280,6480,3240,243,-1336320,-1036800,-401760,-103680,29160,11664,
%U 729,-36126720,-28062720,-10886400,-2812320,-544320,122472,40824,2187,-1114767360,-867041280,-336752640,-87091200
%N Triangular sequence based on the coefficients of the magnetic model for q=1/2: p(x,t)=Exp[x*t]*((t^2 + 1/2 - 1)/(2*t + 1/2 - 2))^2.
%C Row sums are: {1, 11, 81, 267, -3039, -109557, -2837007, -78266997, -2424502719, -84168178677, -3241001149551};
%C These magnetic models are important in the application of nonlinear complex dynamics to physical systems.
%D Peitgen and Richter, eds., The Beauty of Fractals, Springer-Verlag, New York, 1986, page145.
%F p(x,t)=Exp[x*t]*((t^2 + 1/2 - 1)/ (2*t + 1/2-2))^2=Sum[P(x,n)*t^n/n!,{n,0,Infinity}]; out_n,m=3^(n + 2)*n!*Coefficient(P(x,n))
%e {{1},
%e {8, 3},
%e {24, 48, 9},
%e {-192, 216, 216, 27},
%e {-2976, -2304, 1296, 864, 81},
%e {-57600, -44640, -17280, 6480, 3240, 243},
%e {-1336320, -1036800, -401760, -103680, 29160, 11664,729},
%e {-36126720, -28062720, -10886400, -2812320, -544320, 122472, 40824, 2187}, {-1114767360, -867041280, -336752640, -87091200, -16873920, -2612736, 489888, 139968, 6561},
%e {-38645268480, -30098718720, -11705057280, -3030773760, -587865600, -91119168,-11757312, 1889568, 472392, 19683},
%e {-1486356480000, -1159358054400, -451480780800, -117050572800, -22730803200, -3527193600, -455595840, -50388480, 7085880, 1574640, 59049}
%t p[t_] =Exp[x*t]*((t^2 + 1/2 - 1)/(2*t + 1/2 - 2))^2; Table[ ExpandAll[3^(n + 2)*n!*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n]], {n, 0, 10}]; a = Table[3^(n + 2)*n!* CoefficientList[SeriesCoefficient[ Series[p[t], {t, 0, 30}], n], x], {n, 0, 10}]; Flatten[a]
%K tabl,sign
%O 1,2
%A _Roger L. Bagula_, Apr 27 2008