A026005 a(n) = T(4*n,n), where T = Catalan triangle (A008315).

1, 4, 27, 208, 1700, 14364, 123970, 1085760, 9612108, 85795600, 770755843, 6960408624, 63127818572, 574609830760, 5246348656500, 48027225765120, 440671237120764, 4051508174260272, 37315784743418332

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Formula

a(n) = (2n+2)/(3n+2) * C(4n+1, n). - Ralf Stephan, Apr 30 2004

a(n) = C(4n,n)-C(4n,n-2)=A039598(2n,n). - Paul Barry, Apr 21 2009

G.f.: (g-2)*g^2/(3*g-4) where g = 1+x*g^4 is the g.f. of A002293. - Mark van Hoeij, Nov 11 2011

Conjecture: 9*n*(3*n+2)*(3*n+1)*a(n) +12*(-55*n^3-59*n^2+65*n-11)*a(n-1) -32*(4*n-5)*(4*n-3)*(2*n-3)*a(n-2)=0. - R. J. Mathar, May 22 2013

a(n) = Sum_{k=0..n}((n+k+1)*binomial(n+k,k)*binomial(3*n-k,n-k))/(2*n+1). - Vladimir Kruchinin, Dec 02 2016

a(n) ~ 2^(8*n+7/2)*3^(-3*n-5/2)/sqrt(Pi*n). - Ilya Gutkovskiy, Dec 02 2016

Mathematica

Table[(2 n+2)/(3 n+2) Binomial[4 n+1, n], {n, 0, 20}] (* Vaclav Kotesovec, Dec 02 2016 *)

Prog

(PARI) a(n) = (2*n+2)/(3*n+2)*binomial(4*n+1, n)

Crossrefs

Sequence in context: A331796 A193221 A091121 * A059391 A371786 A190738

Adjacent sequences: A026002 A026003 A026004 * A026006 A026007 A026008

Keyword

nonn

Author

Clark Kimberling

Extensions

More terms from Ralf Stephan, Apr 30 2004

Status

approved