A137436 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).
0, 3, 0, 6, 48, 0, 9, 0, 192, 0, 12, 2880, 0, 480, 0, 15, 0, 17280, 0, 960, 0, 18, 362880, 0, 60480, 0, 1680, 0, 21, 0, 2903040, 0, 161280, 0, 2688, 0, 24, 78382080, 0, 13063680, 0, 362880, 0, 4032, 0, 27, 0, 783820800, 0, 43545600, 0, 725760, 0, 5760, 0, 30
Offset: 1
Examples
{0},
{3},
{0, 6},
{48, 0, 9},
{0, 192, 0, 12},
{2880, 0, 480, 0, 15},
{0, 17280, 0, 960, 0, 18},
{362880, 0, 60480, 0, 1680, 0, 21},
{0, 2903040, 0, 161280, 0, 2688, 0, 24},
{78382080, 0, 13063680, 0, 362880, 0, 4032, 0, 27},
{0, 783820800, 0, 43545600, 0, 725760, 0, 5760, 0, 30}
References
- Over and Over Again, Chang and Sederberg,MAA,1997, page 111.
- Peitgen and Richter, eds., The Beauty of Fractals, Springer-Verlag, New York, 1986, page 47, map 7, page 146.
Crossrefs
Cf. A115052.
Programs
-
Mathematica
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]
Formula
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))
Comments