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
3*(n+1)*a(n) + (-17*n-1)*a(n-1) + 10*(2*n-3)*a(n-2) = 0. - R. J. Mathar, Feb 13 2015
-(n+1)*(7*n-6)*a(n) + 2*(7*n+1)*(2*n-1)*a(n-1) = 0. - R. J. Mathar, Feb 13 2015
G.f.: (3 - 5*x - 3*sqrt(1 - 4*x))/(x*sqrt(1 - 4*x)). - Ilya Gutkovskiy, Jun 13 2017
MATHEMATICA
Table[CatalanNumber[n](7n+1), {n, 0, 30}] (* Harvey P. Dale, Jun 01 2024 *)
PROG
(PARI) a(n) = (7*n+1) * binomial(2*n, n)/(n+1) \\ Michel Marcus, Jul 24 2013
(Magma) [Catalan(n)*(7*n+1):n in [0..25] ]; // Marius A. Burtea, Jan 05 2020
(Magma) R<x>:=PowerSeriesRing(Rationals(), 27); (Coefficients(R!( (3-5*x-3*Sqrt(1-4*x))/(x*Sqrt(1 - 4*x))) )); // Marius A. Burtea, Jan 05 2020
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Barry E. Williams, Dec 24 1999
EXTENSIONS
Terms a(21) and beyond from Andrew Howroyd, Jan 02 2020
STATUS
approved