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%I #2 Mar 30 2012 17:34:26
%S 0,3,0,6,48,0,9,0,192,0,12,2880,0,480,0,15,0,17280,0,960,0,18,362880,
%T 0,60480,0,1680,0,21,0,2903040,0,161280,0,2688,0,24,78382080,0,
%U 13063680,0,362880,0,4032,0,27,0,783820800,0,43545600,0,725760,0,5760,0,30
%N Triangular sequence based on the coefficients of the Blaschke product like tan(3u) polynomial function: p(x,t)=Exp[x*t]*(-t)*(3 - t^2)/(-1 + 3*t^2).
%C Row sums are:
%C {0, 3, 6, 57, 204, 3375, 18258, 425061, 3067032, 91812699, 828097950}:
%C The Tan(m*arcTan(t)) functions that recur as nested ( here m=3):
%C f^n(t)=Tan(m^n*arcTan(t));
%C are interesting as Chebyshev like and being related to magnetic models.
%D Over and Over Again, Chang and Sederberg,MAA,1997, page 111.
%D Peitgen and Richter, eds., The Beauty of Fractals, Springer-Verlag, New York, 1986, page 47, map 7, page 146.
%F p(x,t)=Exp[x*t]*(-t)*(3 - t^2)/(-1 + 3*t^2)=Sum[P(x,n)*t^n/n!,{n,0,Infinity}]; out_n,m=n!*Coefficient(P(x,n))
%e {0},
%e {3},
%e {0, 6},
%e {48, 0, 9},
%e {0, 192, 0, 12},
%e {2880, 0, 480, 0, 15},
%e {0, 17280, 0, 960, 0, 18},
%e {362880, 0, 60480, 0, 1680, 0, 21},
%e {0, 2903040, 0, 161280, 0, 2688, 0, 24},
%e {78382080, 0, 13063680, 0, 362880, 0, 4032, 0, 27},
%e {0, 783820800, 0, 43545600, 0, 725760, 0, 5760, 0, 30}
%t p[t_] = Exp[x*t]*(-t)*(3 - t^2)/(-1 + 3*t^2); Table[ ExpandAll[n!*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n]], {n, 0, 10}]; a = Table[n!* CoefficientList[SeriesCoefficient[ Series[p[t], {t, 0, 30}], n], x], {n, 0, 10}]; Flatten[a]
%Y Cf. A115052.
%K nonn,tabl,uned
%O 1,2
%A _Roger L. Bagula_, Apr 27 2008
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