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 A091138 #27 Jan 13 2024 10:52:06
%S A091138 1,2,3,6,15,0,315,1890,-82215,708750,41008275,-1385549550,
%T A091138 -33403344975,3426898600125,26529571443375,-13516476003780750,
%U A091138 157765729690193625,84230651703487038750,-3280917943856839411125,-799561865724400084556250,62859004972802312944044375
%N A091138 E.g.f. A(x) satisfies A(A(x)) = x/(1-x)^2.
%C A091138 First non-integer term is a(30) = 16103946844555056574100466078211185438823359375/2.
%H A091138 R. J. Mathar, <a href="/A091138/b091138.txt">Table of n, a(n) for n = 1..28</a>
%H A091138 Dmitry Kruchinin, Vladimir Kruchinin, <a href="http://arxiv.org/abs/1302.1986">Method for solving an iterative functional equation A^{2^n}(x)=F(x)</a>, arXiv:1302.1986
%F A091138 a(n) = n!* A030274(n)/A030275(n).
%F A091138 a(n) = n!*T(n,1), T(n,m)=1/2*(binomial(n+m-1,2*m-1)-sum(i=m+1..n-1, T(n,i)*T(i,m))), n>m, T(n,n)=1. - _Vladimir Kruchinin_, Mar 14 2012
%t A091138 t[n_, m_] := t[n, m] = If[n == m, 1, 1/2*(Binomial[n+m-1, 2*m-1] - Sum[t[n, i]*t[i, m], {i, m+1, n-1}])]; a[n_] := n!*t[n, 1]; Table[a[n], {n, 1, 21}] (* _Jean-François Alcover_, Feb 26 2013, after _Vladimir Kruchinin_ *)
%o A091138 (Maxima)
%o A091138 T(n,m):=if n=m then 1 else 1/2*(binomial(n+m-1,2*m-1)-sum(T(n,i)*T(i,m),i,m+1,n-1));
%o A091138 makelist(2^(n-1)*T(n,1),n,1,10); /* _Vladimir Kruchinin_, Mar 14 2012 */
%K A091138 easy,frac,fini,sign
%O A091138 1,2
%A A091138 _Vladeta Jovovic_, Dec 20 2003
%E A091138 More terms from _R. J. Mathar_, Apr 28 2007