A066798 - OEIS

%I #23 Apr 04 2020 20:32:26

%S 20,944,49564,2753720,157871240,9233006540,547490880980,

%T 32795094564080,1979734520212192,120244316085073616,

%U 7339672750101339356,449852213026938118560,27666867082225970134160

%N a(n) = Sum_{i=1..n} binomial(6*i,3*i).

%H Harry J. Smith, <a href="/A066798/b066798.txt">Table of n, a(n) for n = 1..100</a>

%F G.f.: (1+8/s)^(3/2)*(s-4)*s^5/(3*(s^4+8*s^3-s+1)*(s^2+4*s-8)) - 1/(1-x) where (s+8)*s^3*x-s+1 = 0. - _Mark van Hoeij_, May 02 2013

%F a(n) ~ sqrt(3) * 64^(n+1) / (189*sqrt(Pi*n)). - _Vaclav Kotesovec_, Jun 07 2019

%p s := RootOf((s+8)*s^3*x-s+1, s):

%p series( (1+8/s)^(3/2)*(s-4)*s^5/(3*(s^4+8*s^3-s+1)*(s^2+4*s-8)) - 1/(1-x), x=0, 30); # _Mark van Hoeij_, May 02 2013

%t Accumulate[Table[Binomial[6n,3n],{n,20}]] (* _Harvey P. Dale_, Apr 04 2020 *)

%o (PARI) { a=0; for (n=1, 100, write("b066798.txt", n, " ", a+=binomial(6*n, 3*n)) ) } \\ _Harry J. Smith_, Mar 28 2010

%Y Cf. A006134, A066796, A066797, A066802.

%K nonn

%O 1,1

%A _Benoit Cloitre_, Jan 18 2002