A051945 a(n) = C(n)*(5n+1) where C(n) = Catalan numbers (A000108).

1, 6, 22, 80, 294, 1092, 4092, 15444, 58630, 223652, 856596, 3292016, 12688732, 49031400, 189885240, 736808220, 2863971270, 11149451940, 43465121700, 169657266240, 662976162420, 2593424304120, 10154564564040, 39794915183400, 156078401826204, 612605246582952

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

(n+1)*(5n-4)*a(n) - 2*(5n+1)(2n-1)*a(n-1) = 0. - R. J. Mathar, Jul 09 2012

G.f.: (2 - 3*x - 2*sqrt(1 - 4*x))/(x*sqrt(1 - 4*x)). - Ilya Gutkovskiy, Jun 13 2017

Mathematica

Table[CatalanNumber[n](5n+1), {n, 0, 30}] (* Harvey P. Dale, Jul 27 2020 *)

Prog

(PARI) a(n) = (5*n+1)*binomial(2*n, n)/(n+1)  \\ Michel Marcus, Jul 12 2013
(Magma) [Catalan(n)*(5*n+1):n in [0..27] ]; // Marius A. Burtea, Jan 05 2020
(Magma) R<x>:=PowerSeriesRing(Rationals(), 29); (Coefficients(R!((2-3*x-2*Sqrt(1-4*x))/(x*Sqrt(1-4*x))))); // Marius A. Burtea, Jan 05 2020

Crossrefs

Column k=5 of A330965.

Cf. A016813, A000108, A051924.

Sequence in context: A111566 A372239 A200052 * A253070 A255461 A003699

Adjacent sequences: A051942 A051943 A051944 * A051946 A051947 A051948

Keyword

easy,nonn

Author

Barry E. Williams, Dec 20 1999

Extensions

Terms a(21) and beyond from Andrew Howroyd, Jan 04 2020

Status

approved