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%I #3 Mar 30 2012 17:34:26
%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
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