A050489 a(n) = C(n)*(10n+1) where C(n) = Catalan numbers (A000108).

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

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)

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.

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