%I #2 Mar 30 2012 17:34:36
%S 1,-1,-1,1,7,-1,-32,-17,2,1,131,263,-11,-1,-522,-2672,-782,153,-16,1,
%T 2073,22868,23108,-2157,187,-1,-8248,-179475,-410608,-61903,18408,
%U -3565,272,1,32887,1342125,5870299,3525859,-524187,79087,-4151,-1,-131318
%N Coefficients of expansion of:p(t,y)=-Exp[t/4]/(-2 + y*Exp[t/4] + y*Exp[3*t/4])
%C Row sums are:
%C {1,-2, 8, -48, 384, -3840, 46080, -645120, 10321920, -185794560, 3715891200,...}
%F p(t,y)=-Exp[t/4]/(-2 + y*Exp[t/4] + y*Exp[3*t/4])
%F The scaling function is:
%F s(y,n)=(1 - y)^(n + 1)*2*(-4)^n*n!
%e {1},
%e {-1, -1},
%e {1, 7},
%e {-1, -32, -17, 2},
%e {1, 131, 263, -11},
%e {-1, -522, -2672, -782, 153, -16},
%e {1, 2073, 22868, 23108, -2157, 187},
%e {-1, -8248, -179475, -410608, -61903, 18408, -3565, 272},
%e {1, 32887, 1342125, 5870299, 3525859, -524187, 79087, -4151},
%e {-1, -131318, -9756650, -74354342, -98711444, -5029394, 3014698, -948050, 129877, -7936},
%e {1, 524789, 69743642, 873642650, 2116045028, 790707644, -166952794, 35456678, -3428005, 151567}
%t Clear[m, n, t, x, y, a]
%t f[t_, y_] = -Exp[t/4]/(-2 + y*Exp[t/4] + y*Exp[3*t/4]) Table[ FullSimplify[ ExpandAll[(1 - y)^(n + 1)*2*(-4)^n* n!*SeriesCoefficient[ Series[f[t, y], {t, 0, 30}], n]]], {n, 0, 10}]
%t a = Table[ CoefficientList[FullSimplify[ExpandAll[( 1 - y)^(n + 1)*2*(-4)^n*n!*SeriesCoefficient[ Series[f[t, y], {t, 0, 30}], n]]], y], {n, 0, 10}]
%t Flatten[a]
%K sign,uned
%O 0,5
%A _Roger L. Bagula_, Dec 18 2009