A026019 a(n) = binomial(3*n,n) - binomial(3*n,n-3).

1, 3, 15, 83, 483, 2898, 17748, 110295, 692967, 4390815, 28009215, 179652564, 1157534420, 7486680048, 48579667704, 316107403839, 2061920664351, 13478362911825, 88272020923485, 579081767982795, 3804622827123195

Offset: 0

Author

Clark Kimberling

Keywords

• nonn
• easy

Crossrefs

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

Programs

Mathematica

Table[Binomial[3n,n]-Binomial[3n,n-3],{n,0,20}] (* Harvey P. Dale, Jun 04 2016 *)

PARI

a(n) = binomial(3*n,n) - binomial(3*n,n-3); \\ Michel Marcus, May 10 2020

Formula

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

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

Extensions

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