login
a(n) = C(n)*(6n+1) where C(n)=Catalan numbers (A000108).
3

%I #26 Sep 08 2022 08:44:58

%S 1,7,26,95,350,1302,4884,18447,70070,267410,1024556,3938662,15184876,

%T 58689100,227327400,882230895,3429693990,13353413370,52062618300,

%U 203235266850,794258570820,3107215911540,12167180964120,47685286297350,187036101361980,734153906619252,2883674432327864,11333968799308652

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

%D A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.

%H Andrew Howroyd, <a href="/A050476/b050476.txt">Table of n, a(n) for n = 0..200</a>

%F 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

%F G.f.: (5 - 8*x - 5*sqrt(1 - 4*x))/(2*x*sqrt(1 - 4*x)). - _Ilya Gutkovskiy_, Jun 13 2017

%t Table[CatalanNumber[n](6n+1),{n,0,20}] (* _Harvey P. Dale_, Nov 05 2011 *)

%o (Magma) [Catalan(n)*(6*n+1):n in [0..27] ]; // _Marius A. Burtea_, Jan 05 2020

%o (Magma) R<x>:=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

%Y Column k=6 of A330965.

%Y Cf. A016861, A000108, A051945.

%K easy,nonn

%O 0,2

%A _Barry E. Williams_, Dec 24 1999