A249691 a(n) = binomial(3*n,n)*(5*n+2)/(2*n+1).

2, 7, 36, 204, 1210, 7371, 45696, 286824, 1817046, 11593725, 74397180, 479634480, 3104160696, 20155648324, 131239189440, 856606186128, 5602957906638, 36716657444145, 241006055925180, 1584293462159100, 10428491209564890

Offset

0,1

Links

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

Formula

G.f.: (sqrt(3)*cotan(y(x))*(1-3*x/(4*sin(y(x))^2))/sqrt(4*x-27*x^2)), where y(x)= arcsin((3^(3/2)*sqrt(x))/2)/3.

a(n) = Sum_{k=0..n} binomial(n,k)*Sum_{j=0..(k+1)} (-1)^(j-k-1) * binomial(k+1,j) *binomial(n+2*j,n+1))).

a(n) ~ 5 * 3^(3*n+1/2) / (sqrt(Pi*n) * 4^(n+1)). - Vaclav Kotesovec, Nov 04 2014

a(n) = sum(k=0..n, binomial(n,k)*(binomial(2*n+2,k+1)-binomial(2*n,k+1))). - Vladimir Kruchinin, Nov 26 2014

2*n*(2*n+1)*(5*n-3)*a(n) -3*(5*n+2)*(3*n-1)*(3*n-2)*a(n-1)=0. - R. J. Mathar, Jun 07 2016

Mathematica

Table[Binomial[3*n, n]*(5*n + 2)/(2*n + 1), {n, 0, 50}] (* G. C. Greubel, Jun 02 2017 *)

Prog

(PARI) for(n=0, 25, print1(binomial(3*n, n)*(5*n+2)/(2*n+1), ", ")) \\ G. C. Greubel, Jun 02 2017

Crossrefs

Sequence in context: A192816 A302895 A302905 * A129261 A371545 A370471

Adjacent sequences: A249688 A249689 A249690 * A249692 A249693 A249694

Keyword

nonn

Author

Vladimir Kruchinin, Nov 04 2014

Extensions

New name from Jean-François Alcover, Nov 26 2014

Status

approved