A026019 - OEIS

%I #20 May 10 2020 17:27:24

%S 1,3,15,83,483,2898,17748,110295,692967,4390815,28009215,179652564,

%T 1157534420,7486680048,48579667704,316107403839,2061920664351,

%U 13478362911825,88272020923485,579081767982795,3804622827123195

%N a(n) = binomial(3*n,n) - binomial(3*n,n-3).

%F G.f.: (1-2*g)*(g^2-g+1)/((3*g-1)*(g-1)^3) where g*(1-g)^2 = x. - _Mark van Hoeij_, Nov 09 2011

%F Conjecture: -2*(2*n+3)*(13*n-9)*(n+1)*a(n) +(499*n^3-7*n^2-120*n-54)*a(n-1) -3*(3*n-5)*(37*n-24)*(3*n-4)*a(n-2)=0. - _R. J. Mathar_, Jun 20 2013

%t Table[Binomial[3n,n]-Binomial[3n,n-3],{n,0,20}] (* _Harvey P. Dale_, Jun 04 2016 *)

%o (PARI) a(n) = binomial(3*n,n) - binomial(3*n,n-3); \\ _Michel Marcus_, May 10 2020

%Y a(n) = T(3n, n), where T is the array defined in A026009.

%K nonn,easy

%O 0,2

%A _Clark Kimberling_

%E More terms from C. Ronaldo (aga_new_ac(AT)hotmail.com), Jan 17 2005