%I
%S 0,1,0,4,0,4,0,64,0,320,0,384,0,7680,0,26880,0,161280,0,195840,
%T 0,3096576,0,10321920,0,43352064,0,263208960,0,319979520,0,
%U 3096576000,0,10218700800,0,40874803200,0,173717913600,0,1055932416000,0,1283840409600
%N Triangular sequence of coefficients from the expansion of p(x,t)=Tan(x*t)/Tan(t).
%C Row sums are: {1, 0, 0, 0, 0, 0, ...};
%F p(x,t)=Tan(x*t)/Tan(t)=Sum[P(x,n)*t^n/n!,{n,0,Infinity}]; out_n,m=(n+1)!*n!*Coefficients(p(x,n)) for even n.
%e {0, 1},
%e {0, 4, 0, 4},
%e {0, 64, 0, 320, 0, 384},
%e {0, 7680, 0, 26880, 0, 161280, 0, 195840},
%e {0, 3096576, 0, 10321920, 0, 43352064, 0, 263208960, 0, 319979520},
%e {0, 3096576000, 0, 10218700800, 0, 40874803200, 0, 173717913600, 0, 1055932416000, 0, 1283840409600}
%t p[t_] = Tan[x*t]/Tan[t]; Table[ ExpandAll[(n+1)!*n!*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n]], {n, 0, 10,2}]; a = Table[ CoefficientList[(n+1)!*n!*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n], x], {n, 0, 10}]; Flatten[a]
%K tabf,sign
%O 1,4
%A _Roger L. Bagula_, Apr 27 2008
