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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..200

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)

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

CROSSREFS

Column k=10 of A330965.

Cf. A017173, A027810, A000108.

Sequence in context: A213772 A062517 A027978 * A156533 A228811 A096638

Adjacent sequences:  A050486 A050487 A050488 * A050490 A050491 A050492

KEYWORD

easy,nonn

AUTHOR

Barry E. Williams, Dec 27 1999

EXTENSIONS

Corrected and extended by Harvey P. Dale, Jul 19 2011

STATUS

approved

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Last modified September 19 06:16 EDT 2020. Contains 337177 sequences. (Running on oeis4.)