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
The Hankel determinant transform is A025172(n-1). - Michael Somos, Sep 17 2006
-(n+1)*(4*n-3)*a(n) + 2*(4*n+1)*(2*n-1)*a(n-1) = 0. - R. J. Mathar, Nov 19 2014
G.f.: (3 - 4*x - 3*sqrt(1 - 4*x))/(2*x*sqrt(1 - 4*x)). - Ilya Gutkovskiy, Jun 13 2017
MATHEMATICA
Table[CatalanNumber[n](4n+1), {n, 0, 30}] (* Harvey P. Dale, Feb 21 2022 *)
PROG
(PARI) {a(n)=if(n<0, 0, (4*n+1)*binomial(2*n, n)/(n+1))} /* Michael Somos, Sep 17 2006 */
(Magma) [Catalan(n)*(4*n+1):n in [0..30] ]; // Marius A. Burtea, Jan 05 2020
(Magma) R<x>:=PowerSeriesRing(Rationals(), 30); (Coefficients(R!( (3 - 4*x - 3*Sqrt(1 - 4*x))/(2*x*Sqrt(1 - 4*x)))) ); // Marius A. Burtea, Jan 05 2020
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Barry E. Williams, Dec 20 1999
EXTENSIONS
Terms a(21) and beyond from Andrew Howroyd, Jan 02 2020
STATUS
approved