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

0,1

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

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

Mathematica

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

Prog

(PARI) for(n=0, 30, print1(((5*n+2)/(n+1))*binomial(2*n, n), ", ")) \\ G. C. Greubel, May 25 2018
(Magma) [((5*n+2)/(n+1))*Binomial(2*n, n): n in [0..30]]; // G. C. Greubel, May 25 2018

Crossrefs

Cf. A000108, A050960.

Sequence in context: A369296 A297345 A052986 * A141753 A014300 A128086

Adjacent sequences: A053365 A053366 A053367 * A053369 A053370 A053371

Keyword

easy,nonn

Author

Barry E. Williams, Jan 06 2000

Extensions

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

Status

approved