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A098444
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Expansion of 1/sqrt(1-6x-11x^2).
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2
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1, 3, 19, 117, 771, 5193, 35629, 247467, 1734931, 12250953, 87006249, 620818047, 4447016781, 31959556983, 230331965379, 1664043517557, 12047551338771, 87387014213433, 634918255153369, 4619923954541247, 33661450900419001
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OFFSET
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0,2
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COMMENTS
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Coefficient of x^n in (1 + 3 x + 5 x^2)^n = number of paths from the origin to (n,0) with steps U=(1,1), H=(1,0) and D=(1,-1); U can have 5 colors and H can have 3 colors. - N-E. Fahssi, Jan 28 2008
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LINKS
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FORMULA
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E.g.f.: exp(3x)*BesselI(0, 2*sqrt(5)*x)
D-finite with recurrence: n*a(n) = 3*(2*n-1)*a(n-1) + 11*(n-1)*a(n-2). - Vaclav Kotesovec, Oct 15 2012
a(n) ~ sqrt(50+15*sqrt(5))*(3+2*sqrt(5))^n/(10*sqrt(Pi*n)). - Vaclav Kotesovec, Oct 15 2012
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MATHEMATICA
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Table[SeriesCoefficient[1/Sqrt[1-6*x-11*x^2], {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 15 2012 *)
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PROG
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(PARI) x='x+O('x^66); Vec(1/sqrt(1-6*x-11*x^2)) \\ Joerg Arndt, May 11 2013
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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