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A051944 a(n) = C(n)*(4n+1) where C(n) = Catalan numbers (A000108). 4
1, 5, 18, 65, 238, 882, 3300, 12441, 47190, 179894, 688636, 2645370, 10192588, 39373700, 152443080, 591385545, 2298248550, 8945490510, 34867625100, 136079265630, 531693754020, 2079632696700, 8141948163960, 31904544069450, 125120702290428, 491056586546652 (list; graph; refs; listen; history; text; internal format)
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

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

Column k=4 of A330965.

Cf. A016777, A000108, A051924.

Sequence in context: A222373 A147535 A184309 * A153373 A225015 A166677

Adjacent sequences:  A051941 A051942 A051943 * A051945 A051946 A051947

KEYWORD

easy,nonn

AUTHOR

Barry E. Williams, Dec 20 1999

EXTENSIONS

Terms a(21) and beyond from Andrew Howroyd, Jan 02 2020

STATUS

approved

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Last modified September 24 21:35 EDT 2020. Contains 337322 sequences. (Running on oeis4.)