This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A079590 #26 Aug 21 2025 16:49:45
%S A079590 1,7,78,969,12650,169911,2324784,32224114,450978066,6358402050,
%T A079590 90177170226,1285063345176,18385569737808,263926640438545,
%U A079590 3799541229226200,54834293825867556,793067310934426018
%N A079590 a(n) = C(6*n+1,n).
%C A079590 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 A079590 Vincenzo Librandi, <a href="/A079590/b079590.txt">Table of n, a(n) for n = 0..200</a>
%F A079590 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 A079590 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 A079590 seq(binomial(6*n+1,n), n = 1 .. 100); # _Robert Israel_, Aug 07 2014
%t A079590 Table[Binomial[6 n + 1, n], {n, 0, 20}] (* _Vincenzo Librandi_, Aug 07 2014 *)
%o A079590 (Magma) [Binomial(6*n+1, n): n in [0..20]]; // _Vincenzo Librandi_, Aug 07 2014
%Y A079590 Cf. A052203.
%K A079590 nonn,changed
%O A079590 0,2
%A A079590 _Benoit Cloitre_, Jan 26 2003