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 A180399 #13 Jun 01 2013 10:03:39
%S A180399 0,1,4,21,138,999,7683,61542,507663,4281849,36748998,319845591,
%T A180399 2816007714,25032803841,224355173193,2024955168606,18388543939947,
%U A180399 167882583075453,1540000362501702,14186252492098011,131176523761136568,1217094112710349731,11327464549934673309
%N A180399 Expansion of (1/3)*(1 - (1-9*x-9*x^2)^(1/3)).
%H A180399 Vincenzo Librandi, <a href="/A180399/b180399.txt">Table of n, a(n) for n = 0..200</a>
%F A180399 G.f.: (1/3)*(1 - (1-9*x-9*x^2)^(1/3)).
%F A180399 a(n) = sum(m=1..n, binomial(m,n-m)/m * sum(k=0..m-1, binomial(k,m-1-k) * 3^k*(-1)^(m-1-k) * binomial(m+k-1,m-1))). [From _Vladimir Kruchinin_, Feb 08 2011]
%F A180399 Recurrence: n*a(n) = 3*(3*n-4)*a(n-1) + 3*(3*n-8)*a(n-2). - _Vaclav Kotesovec_, Oct 20 2012
%F A180399 a(n) ~ ((13-3*sqrt(13))/2)^(1/3)/(9*Gamma(2/3)) * ((9+3*sqrt(13))/2)^n/(n^(4/3)). - _Vaclav Kotesovec_, Oct 20 2012
%e A180399 The Maclaurin series begins with x + 4x^2 + 21x^3.
%t A180399 CoefficientList[Series[1/3*(1-(1-9*x-9*x^2)^(1/3)), {x, 0, 20}], x] (* _Vaclav Kotesovec_, Oct 20 2012 *)
%o A180399 (PARI) x='x+O('x^66); concat([0],Vec(1/3*(1-(1-9*x-9*x^2)^(1/3)))) \\ _Joerg Arndt_, Jun 01 2013
%Y A180399 Cf. A180400.
%K A180399 nonn
%O A180399 0,3
%A A180399 _Clark Kimberling_, Sep 01 2010