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 A386229 #12 Jul 16 2025 10:12:29
%S A386229 1,3,12,70,535,4908,51478,600584,7662285,105684465,1563183259,
%T A386229 24645719004,412279514088,7290426692472,135862518564330,
%U A386229 2661378323466016,54675576786754501,1175673956931922257,26411686616265112230,618863341216409971750,15101129008183181824938
%N A386229 G.f. A(x) satisfies A(x) = 1/( (1-x)^2 * (1 - x*A(x) - x^2*A'(x)) ).
%F A386229 a(n) = (n+1) * (1 + 1/2 * Sum_{k=0..n-1} a(k) * a(n-1-k)).
%F A386229 a(n) = n + 1 + Sum_{k=0..n-1} (1 + k) * a(k) * a(n-1-k).
%t A386229 terms = 21; A[_] = 1; Do[A[x_] = 1/((1-x)^2(1-x*A[x]-x^2*A'[x])) + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* _Stefano Spezia_, Jul 16 2025 *)
%o A386229 (PARI) a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=(i+1)*(1+sum(j=0, i-1, v[j+1]*v[i-j])/2)); v;
%Y A386229 Cf. A088716, A321087, A386230.
%Y A386229 Cf. A386211.
%K A386229 nonn
%O A386229 0,2
%A A386229 _Seiichi Manyama_, Jul 16 2025