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A050489
a(n) = C(n)*(10n+1) where C(n) = Catalan numbers (A000108).
3
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
OFFSET
0,2
REFERENCES
Albert H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
LINKS
FORMULA
-(n+1)*(10*n-9)*a(n) + 2*(10*n+1)*(2*n-1)*a(n-1) = 0. - R. J. Mathar, Dec 03 2014
From Stefano Spezia, Feb 16 2020: (Start)
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
MATHEMATICA
Table[CatalanNumber[n](10n+1), {n, 0, 30}] (* Harvey P. Dale, Jul 19 2011 *)
PROG
(Magma) [Catalan(n)*(10*n+1):n in [0..30] ]; // Marius A. Burtea, Jan 05 2020
(PARI) a(n)=binomial(2*n, n)/(n+1)*(10*n+1) \\ Charles R Greathouse IV, Oct 23 2023
CROSSREFS
Column k=10 of A330965.
Sequence in context: A213772 A062517 A027978 * A156533 A228811 A096638
KEYWORD
easy,nonn
AUTHOR
Barry E. Williams, Dec 27 1999
EXTENSIONS
Corrected and extended by Harvey P. Dale, Jul 19 2011
STATUS
approved