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 A104859 #24 Jul 26 2021 01:48:55
%S A104859 1,2,5,17,72,345,1773,9525,52788,299463,1730178,10144818,60211926,
%T A104859 361042498,2183809018,13308564682,81637319641,503667864976,
%U A104859 3123298907641,19456221197941,121696331095636,764008782313381
%N A104859 Partial sums of A001764.
%H A104859 Vincenzo Librandi, <a href="/A104859/b104859.txt">Table of n, a(n) for n = 0..200</a>
%F A104859 a(n) = Sum_{k=0..n} binomial(3k, k)/(2k+1).
%F A104859 G.f.: T(z)/(1-z), where T = 1+z*T^3.
%F A104859 G.f.: 2*sin((1/3)*arcsin(sqrt(27*z/4)))/((1-z)*sqrt(3*z)).
%F A104859 Recurrence: 2*(2*n^2 + 9*n + 10)*a(n+2) - (31*n^2 + 99*n + 80)*a(1+n) + 3*(9*n^2 + 27*n + 20)*a(n) = 0. - _Emanuele Munarini_, Apr 08 2011
%F A104859 a(n) ~ 3^(3*n+7/2)/(23*sqrt(Pi)*2^(2*n+2)*n^(3/2)). - _Vaclav Kotesovec_, Oct 17 2012
%F A104859 G.f. A(x) satisfies: A(x) = 1 / (1 - x) + x * (1 - x)^2 * A(x)^3. - _Ilya Gutkovskiy_, Jul 25 2021
%p A104859 a:=n->add(binomial(3*k,k)/(2*k+1),k=0..n): seq(a(n),n=0..26);
%t A104859 Table[Sum[Binomial[3k,k]/(2k+1),{k,0,n}],{n,0,20}] (* _Emanuele Munarini_, Apr 08 2011 *)
%o A104859 (Maxima) makelist(sum(binomial(3*k,k)/(2*k+1),k,0,n),n,0,20); /* _Emanuele Munarini_, Apr 08 2011 */
%Y A104859 Cf. A001764.
%K A104859 nonn,easy
%O A104859 0,2
%A A104859 _Emeric Deutsch_, Apr 24 2005