A053368 a(n) = (5n+2)*C(n) where C(n) = Catalan numbers (A000108).

2, 7, 24, 85, 308, 1134, 4224, 15873, 60060, 228514, 873392, 3350802, 12896744, 49774300, 192559680, 746503065, 2899328940, 11279096730, 43942760400, 171424529430, 669540282840, 2617890571140, 10246047127680, 40137974797050, 157368305973528, 617467192984404, 2424490605524064

Offset: 0

Author

Barry E. Williams, Jan 06 2000

Keywords

• easy
• nonn

References

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

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A000108, A050960.

Programs

Magma

[((5*n+2)/(n+1))*Binomial(2*n,n): n in [0..30]]; // G. C. Greubel, May 25 2018

Mathematica

Table[(5*n + 2)*CatalanNumber[n], {n, 0, 50}] (* G. C. Greubel, May 25 2018 *)

PARI

for(n=0,30, print1(((5*n+2)/(n+1))*binomial(2*n,n), ", ")) \\ G. C. Greubel, May 25 2018

Formula

From R. J. Mathar, Feb 13 2015: (Start)

3*(n+1)*a(n) + 2*(-7*n-2)*a(n-1) + 4*(2*n-3)*a(n-2) = 0.

-(n+1)*(5*n-3)*a(n) + 2*(5*n+2)*(2*n-1)*a(n-1) = 0. (End)

G.f.: (3 - 2*x - 3*sqrt(1 - 4*x))/(2*x*sqrt(1 - 4*x)). - Amiram Eldar, Jul 08 2023

Extensions

Terms a(21) onward added by G. C. Greubel, May 25 2018