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A050477
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a(n) = C(n)*(7n+1) where C(n)=Catalan numbers (A000108).
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2
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1, 8, 30, 110, 406, 1512, 5676, 21450, 81510, 311168, 1192516, 4585308, 17681020, 68346800, 264769560, 1027653570, 3995416710, 15557374800, 60660114900, 236813267460, 925540979220, 3621007518960, 14179797364200, 55575657411300, 217993800897756, 855702566655552
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OFFSET
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0,2
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REFERENCES
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A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
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LINKS
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FORMULA
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3*(n+1)*a(n) + (-17*n-1)*a(n-1) + 10*(2*n-3)*a(n-2) = 0. - R. J. Mathar, Feb 13 2015
-(n+1)*(7*n-6)*a(n) + 2*(7*n+1)*(2*n-1)*a(n-1) = 0. - R. J. Mathar, Feb 13 2015
G.f.: (3 - 5*x - 3*sqrt(1 - 4*x))/(x*sqrt(1 - 4*x)). - Ilya Gutkovskiy, Jun 13 2017
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MATHEMATICA
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Table[CatalanNumber[n](7n+1), {n, 0, 30}] (* Harvey P. Dale, Jun 01 2024 *)
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PROG
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(PARI) a(n) = (7*n+1) * binomial(2*n, n)/(n+1) \\ Michel Marcus, Jul 24 2013
(Magma) R<x>:=PowerSeriesRing(Rationals(), 27); (Coefficients(R!( (3-5*x-3*Sqrt(1-4*x))/(x*Sqrt(1 - 4*x))) )); // Marius A. Burtea, Jan 05 2020
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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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EXTENSIONS
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STATUS
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approved
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