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Search: id:A137436
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| A137436 |
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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). |
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+0
1
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| 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
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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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.
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REFERENCES
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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.
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FORMULA
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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))
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EXAMPLE
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{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}
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MATHEMATICA
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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]
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CROSSREFS
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Cf. A115052.
Sequence in context: A059684 A083350 A002043 this_sequence A099893 A135534 A077896
Adjacent sequences: A137433 A137434 A137435 this_sequence A137437 A137438 A137439
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KEYWORD
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nonn,tabl,uned
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 27 2008
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