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A026005 a(n) = T(4*n,n), where T = Catalan triangle (A008315). 1
1, 4, 27, 208, 1700, 14364, 123970, 1085760, 9612108, 85795600, 770755843, 6960408624, 63127818572, 574609830760, 5246348656500, 48027225765120, 440671237120764, 4051508174260272, 37315784743418332 (list; graph; refs; listen; history; text; internal format)
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: A091125 A193221 A091121 * A059391 A190738 A275607

Adjacent sequences:  A026002 A026003 A026004 * A026006 A026007 A026008

KEYWORD

nonn

AUTHOR

Clark Kimberling

EXTENSIONS

More terms from Ralf Stephan, Apr 30 2004

STATUS

approved

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Last modified September 17 06:41 EDT 2019. Contains 327119 sequences. (Running on oeis4.)