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%I #14 Dec 11 2019 07:00:24
%S 0,1,0,-2,0,2,0,24,0,-40,0,16,0,-720,0,1568,0,-1120,0,272,0,40320,0,
%T -104704,0,102144,0,-45696,0,7936,0,-3628800,0,10720512,0,-12869120,0,
%U 8042496,0,-2618880,0,353792,0,479001600,0,-1565051904,0,2188865536,0,-1712668672,0,789854208,0,-202369024,0
%N Triangle read by rows: coefficients from the expansion of p(x,t) = tan(x*arctan(t)) which is in the Chebyshevlike form: T(t,x) = cos(x*arccos(t)).
%C Row sums are {1, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...}.
%C The polynomials are not orthogonal on a Chebyshev weighted domain.
%D Chang and Sederberg, Over and Over Again, MAA, 1997, page 111.
%F T(n,m) = n! * coefficients(p(x,n)), odd-indexed terms only, where p(x,t) = tan(x*arctan(t)) = Sum_{n>=0} P(x,n)*t^n/n!.
%e {0, 1},
%e {0, -2, 0, 2},
%e {0, 24, 0, -40, 0, 16},
%e {0, -720, 0, 1568, 0, -1120, 0, 272},
%e {0, 40320, 0, -104704, 0, 102144, 0, -45696, 0, 7936},
%e {0, -3628800, 0, 10720512, 0, -12869120, 0, 8042496, 0, -2618880, 0, 353792}, {0, 479001600, 0, -1565051904, 0, 2188865536, 0, -1712668672, 0, 789854208, 0, -202369024, 0, 22368256},
%e {0, -87178291200,0, 309188763648, 0, -487356047360, 0, 450481647616,0, -263012372480, 0, 96327655424, 0, -20355112960, 0, 1903757312},
%e {0, 20922789888000, 0, -79493016453120, 0, 138125290635264, 0, -145543597588480, 0, 101310804328448, 0, -47338162094080, 0, 14395135885312, 0, -2589109944320, 0, 209865342976},
%e {0, -6402373705728000, 0, 25804966598737920, 0,-48657759347146752, 0, 57064887390568448, 0, -45634645720694784, 0, 25589689363070976, 0, -9984529525374976, 0, 2597395096141824, 0, -406719034687488, 0, 29088885112832}
%t p[t_] = Tan[x*ArcTan[t]];
%t g = Table[ ExpandAll[n!*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n]], {n, 1, 20, 2}];
%t a = Table[ CoefficientList[n!*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n], x], {n, 1, 20, 2}];
%t Flatten[a]
%K tabf,sign
%O 1,4
%A _Roger L. Bagula_, Apr 27 2008
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