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A098264
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G.f.: 1/(1-2x-19x^2)^(1/2).
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7
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1, 1, 11, 31, 211, 851, 4901, 22961, 124531, 623011, 3313201, 17086301, 90453661, 473616781, 2509264811, 13250049551, 70368250451, 373539254611, 1989045489281, 10597110956861, 56566637447401, 302196871378601, 1616570627763311, 8654955238504531, 46384344189261661
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OFFSET
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0,3
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COMMENTS
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Central coefficient of (1+x+5x^2)^n.
Also number of paths from (0,0) to (n,0) using steps U=(1,1), H=(1,0) and D=(1,-1), the U steps can have five colors. - N-E. Fahssi, Mar 31 2008
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LINKS
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FORMULA
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E.g.f. : exp(x)*BesselI(0, 2*sqrt(5)x).
a(n) = sum{k=0..floor(n/2), binomial(n, k)*binomial(n-k, k)*5^k}.
a(n) = sum{k=0..floor(n/2), binomial(n, 2k)*binomial(2k, k)*5^k}.
n*a(n) +(1-2*n)*a(n-1) +19*(1-n)*a(n-2)=0. - R. J. Mathar, Nov 14 2011
a(n) ~ sqrt(50+5*sqrt(5))*(1+2*sqrt(5))^n/(10*sqrt(Pi*n)). - Vaclav Kotesovec, Oct 14 2012
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MATHEMATICA
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Table[SeriesCoefficient[1/Sqrt[1-2*x-19*x^2], {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 14 2012 *)
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PROG
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(PARI) x='x+O('x^66); Vec(1/(1-2*x-19*x^2)^(1/2)) \\ 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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