A050479 a(n) = C(n)*(9n+1) where C(n)=Catalan numbers (A000108).

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

Andrew Howroyd, Table of n, a(n) for n = 0..200

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.

Cf. A017077, A000108, A051945.

Sequence in context: A027982 A064603 A164298 * A288391 A220206 A218081

Adjacent sequences: A050476 A050477 A050478 * A050480 A050481 A050482

Keyword

easy,nonn

Author

Barry E. Williams, Dec 24 1999

Extensions

Terms a(21) and beyond from Andrew Howroyd, Jan 05 2020

Status

approved