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A051945 a(n) = C(n)*(5n+1) where C(n) = Catalan numbers (A000108). 7
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 (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

(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: A217530 A111566 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

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Last modified July 24 11:17 EDT 2021. Contains 346273 sequences. (Running on oeis4.)