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

1,2

Comments

Row sums are:

{0, 3, 6, 57, 204, 3375, 18258, 425061, 3067032, 91812699, 828097950}:

The Tan(m*arcTan(t)) functions that recur as nested ( here m=3):

f^n(t)=Tan(m^n*arcTan(t));

are interesting as Chebyshev like and being related to magnetic models.

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.

Links

Table of n, a(n) for n=1..56.

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))

Example

{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}

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]

Crossrefs

Cf. A115052.

Sequence in context: A083350 A002043 A171002 * A099893 A135534 A346516

Adjacent sequences: A137433 A137434 A137435 * A137437 A137438 A137439

Keyword

nonn,tabl,uned

Author

Roger L. Bagula, Apr 27 2008

Status

approved