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A050489
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a(n) = C(n)*(10n+1) where C(n) = Catalan numbers (A000108).
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3
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1, 11, 42, 155, 574, 2142, 8052, 30459, 115830, 442442, 1696396, 6525246, 25169452, 97319900, 377096040, 1463921595, 5692584870, 22169259090, 86452604700, 337547269290, 1319388204420, 5162382341220, 20217646564440, 79246770753150, 310866899505084
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OFFSET
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0,2
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REFERENCES
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Albert 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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-(n+1)*(10*n-9)*a(n) + 2*(10*n+1)*(2*n-1)*a(n-1) = 0. - R. J. Mathar, Dec 03 2014
O.g.f.: 2*(1 + sqrt(1 - 4*x) + 16*x)/((1 + sqrt(1 - 4*x))^2*sqrt(1 - 4*x)).
E.g.f.: exp(2*x)*(I_0(2*x) + 9*I_1(2*x)), where I_n(x) is the modified Bessel function of the first kind.
(End)
G.f.: (9 - 16*x - 9*sqrt(1 - 4*x))/(2*x*sqrt(1 - 4*x)). - Amiram Eldar, Jul 08 2023
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MATHEMATICA
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Table[CatalanNumber[n](10n+1), {n, 0, 30}] (* Harvey P. Dale, Jul 19 2011 *)
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PROG
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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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