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A098272
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2^(2n+1) * C(3n,n)/(2n+1).
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2
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2, 8, 96, 1536, 28160, 559104, 11698176, 254017536, 5670567936, 129328742400, 3000426823680, 70587116421120, 1679973370822656, 40376795886780416, 978590323955466240, 23890230876435382272, 586939535850605641728
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..100
M. Bousquet-M\'elou, Walks in the quarter plane: Kreweras' algebraic model
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FORMULA
| G.f. satisfies A(x) = Sum[n>=0, a(n)*x^(3n+1)] = x(2+A(x)^3).
G.f.: (2 Sin[1/3*ArcSin[3*Sqrt[3]*Sqrt[x]]])/(Sqrt[3]*Sqrt[x]) [From Harvey P. Dale, Oct 02 2011]
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MATHEMATICA
| Table[2^(2n+1) Binomial[3n, n]/(2n+1), {n, 0, 20}](* From Harvey P. Dale, Oct 02 2011 *)
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PROG
| (PARI) a(n)=2^(2*n+1)*binomial(3*n, n)/(2*n+1)
(PARI) a(n)=polcoeff(serreverse(Ser(x/(2+x^3))), 3*n+1)
(MAGMA) [2^(2*n+1)*Binomial(3*n, n)/(2*n+1): n in [0..20]]; // Vincenzo Librandi, Oct 03 2011
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CROSSREFS
| Equals 2n * A006335(n) = 2^(2n+1) * A001764(n).
Sequence in context: A131349 A067964 A126429 * A087540 A052713 A136797
Adjacent sequences: A098269 A098270 A098271 * A098273 A098274 A098275
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KEYWORD
| nonn
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AUTHOR
| Ralf Stephan, Sep 02 2004
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