A050476 a(n) = C(n)*(6*n + 1) where C(n) = Catalan numbers (A000108).

1, 7, 26, 95, 350, 1302, 4884, 18447, 70070, 267410, 1024556, 3938662, 15184876, 58689100, 227327400, 882230895, 3429693990, 13353413370, 52062618300, 203235266850, 794258570820, 3107215911540, 12167180964120, 47685286297350, 187036101361980, 734153906619252, 2883674432327864, 11333968799308652

Offset: 0

Author

Barry E. Williams, Dec 24 1999

Keywords

• easy
• nonn
• changed

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

Crossrefs

Column k=6 of A330965.

Cf. A016861, A000108, A051945.

Programs

Magma

[Catalan(n)*(6*n+1):n in [0..27] ]; // Marius A. Burtea, Jan 05 2020

Magma

R:=PowerSeriesRing(Rationals(),30); (Coefficients(R!( (5-8*x-5*Sqrt(1-4*x))/(2*x*Sqrt(1-4*x))))); // Marius A. Burtea, Jan 05 2020

Mathematica

Table[CatalanNumber[n](6n+1),{n,0,20}] (* Harvey P. Dale, Nov 05 2011 *)

Formula

5*(n+1)*a(n) + 2*(-14*n-1)*a(n-1) + 16*(2*n-3)*a(n-2) = 0. - R. J. Mathar, Feb 04 2015

G.f.: (5 - 8*x - 5*sqrt(1 - 4*x))/(2*x*sqrt(1 - 4*x)). - Ilya Gutkovskiy, Jun 13 2017

From Peter Bala, Aug 23 2025: (Start)

a(n) = binomial(2*n, n) + 5*binomial(2*n, n-1) = A000984(n) + 5*A001791(n).

a(n) ~ 4^n * 6/sqrt(Pi*n). (End)