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A050479
a(n) = C(n)*(9n+1) where C(n)=Catalan numbers (A000108).
2
1, 10, 38, 140, 518, 1932, 7260, 27456, 104390, 398684, 1528436, 5878600, 22673308, 87662200, 339653880, 1318498920, 5126862150, 19965297660, 77855108100, 303969268680, 1188105796020, 4648590733800, 18205030164360, 71356399639200, 279909199969308, 1098799886728152
OFFSET
0,2
REFERENCES
A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
LINKS
FORMULA
4*(n+1)*a(n) + (-23*n-1)*a(n-1) + 14*(2*n-3)*a(n-2) = 0. - R. J. Mathar, Feb 13 2015
-(n+1)*(9*n-8)*a(n) + 2*(9*n+1)*(2*n-1)*a(n-1) = 0. - R. J. Mathar, Feb 13 2015
G.f.: (4 - 7*x - 4*sqrt(1 - 4*x))/(x*sqrt(1 - 4*x)). - Ilya Gutkovskiy, Jun 13 2017
PROG
(Magma) [Catalan(n)*(9*n+1):n in [0..27] ]; // Marius A. Burtea, Jan 05 2020
(Magma) R<x>:=PowerSeriesRing(Rationals(), 30); (Coefficients(R!( (4-7*x-4*Sqrt(1-4*x))/(x*Sqrt(1-4*x)))))// Marius A. Burtea, Jan 05 2020
CROSSREFS
Column k=9 of A330965.
Sequence in context: A027982 A064603 A164298 * A288391 A220206 A218081
KEYWORD
easy,nonn
AUTHOR
Barry E. Williams, Dec 24 1999
EXTENSIONS
Terms a(21) and beyond from Andrew Howroyd, Jan 05 2020
STATUS
approved