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 A386211 #20 Aug 05 2025 04:54:42
%S A386211 1,2,5,18,89,556,4127,35084,334049,3510574,40300769,501455462,
%T A386211 6721438253,96561557816,1480441163151,24132225315816,416852189961737,
%U A386211 7607668036964506,146296367990498941,2957053490913146762,62682940163232269033,1390605993609167492932
%N A386211 G.f. A(x) satisfies A(x) = 1/(1-x)^2 + x^2*A(x)*A'(x).
%H A386211 Vaclav Kotesovec, <a href="/A386211/b386211.txt">Table of n, a(n) for n = 0..446</a>
%F A386211 a(n) = n + 1 + (n-1)/2 * Sum_{k=0..n-1} a(k) * a(n-1-k).
%F A386211 a(n) = n + 1 + Sum_{k=0..n-1} k * a(k) * a(n-1-k).
%F A386211 a(n) ~ c * n! * n, where c = 1.4406730618690233665395265348... - _Vaclav Kotesovec_, Aug 05 2025
%t A386211 terms = 22; A[_] = 1; Do[A[x_] = 1/(1-x)^2+x^2*A[x]A'[x] + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* _Stefano Spezia_, Jul 16 2025 *)
%o A386211 (PARI) a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=i+1+(i-1)/2*sum(j=0, i-1, v[j+1]*v[i-j])); v;
%Y A386211 Cf. A143917, A386212.
%Y A386211 Cf. A386209.
%K A386211 nonn
%O A386211 0,2
%A A386211 _Seiichi Manyama_, Jul 15 2025