%I #22 Sep 08 2022 08:45:08
%S 1,7,78,969,12650,169911,2324784,32224114,450978066,6358402050,
%T 90177170226,1285063345176,18385569737808,263926640438545,
%U 3799541229226200,54834293825867556,793067310934426018
%N C(6n+1,n).
%C a(n) is the number of paths from (0,0) to (6n,n) taking north and east steps and avoiding north^{=2}. - _Shanzhen Gao_, Apr 15 2010
%H Vincenzo Librandi, <a href="/A079590/b079590.txt">Table of n, a(n) for n = 0..200</a>
%F a(n) is asymptotic to c*sqrt(n)*(46656/3125)^n with c= 0.5243... [c = 2*3^(3/2)/(5^(3/2)*sqrt(Pi)) = 0.52442324668419795386... - _Vaclav Kotesovec_, Feb 14 2019]
%F G.f.: hypergeom([1/3, 1/2, 2/3, 5/6, 7/6], [2/5, 3/5, 4/5, 6/5], (46656/3125)*x). - _Robert Israel_, Aug 07 2014
%p seq(binomial(6*n+1,n), n = 1 .. 100); # _Robert Israel_, Aug 07 2014
%t Table[Binomial[6 n + 1, n], {n, 0, 20}] (* _Vincenzo Librandi_, Aug 07 2014 *)
%o (Magma) [Binomial(6*n+1, n): n in [0..20]]; // _Vincenzo Librandi_, Aug 07 2014
%Y Cf. A052203.
%K nonn
%O 0,2
%A _Benoit Cloitre_, Jan 26 2003