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A259613
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a(n) = binomial(6*n,2*n)/3, n>0, a(0)=1.
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1
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1, 5, 165, 6188, 245157, 10015005, 417225900, 17620076360, 751616304549, 32308782859535, 1397281501935165, 60727722660586800, 2650087220696342700, 116043807643289338428, 5096278545356362962504, 224377658168860057076688
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OFFSET
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0,2
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 0..600
V. V. Kruchinin and D. V. Kruchinin, A Generating Function for the Diagonal T_{2n,n} in Triangles, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.6
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FORMULA
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G.f.: A(x) = 1 + (x*B(x)')/(B(x)) where B(x) = 2 * (1 + x*B(x)^2)^2 / (1 - 2*x*B(x)^2 + sqrt(1-8*x*B(x)^2)).
a(n) ~ 3^(6*n-1/2) / (sqrt(Pi*n) * 2^(4*n+3/2)). - Vaclav Kotesovec, Jul 01 2015
a(n) = A025174(2*n), n>0. - R. J. Mathar, Jun 07 2016
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MATHEMATICA
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Join[{1}, Table[Binomial[6 n, 2 n]/3, {n, 30}]] (* Vincenzo Librandi, Jul 01 2015 *)
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PROG
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(PARI) vector(20, n, n--; if (n==0, 1, binomial(6*n, 2*n)/3)) \\ Michel Marcus, Jul 01 2015
(Magma) [1] cat [Binomial(6*n, 2*n)/3: n in [1..20]]; // Vincenzo Librandi, Jul 01 2015
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CROSSREFS
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Cf. A182959.
Sequence in context: A317456 A203185 A129995 * A047940 A229414 A210923
Adjacent sequences: A259610 A259611 A259612 * A259614 A259615 A259616
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KEYWORD
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nonn
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AUTHOR
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Vladimir Kruchinin, Jun 30 2015
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STATUS
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approved
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