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 A385762 #11 Jul 09 2025 10:14:28
%S A385762 1,1,2,9,80,1204,27788,918831,41389972,2443323132,183303840972,
%T A385762 17050267807478,1926895029660880,260150110806399232,
%U A385762 41365993162914888760,7652990621445212758255,1630131235132495370561820,396129991240222795968202788,108937459572870420021782788268
%N A385762 G.f. A(x) satisfies A(x) = 1/(1 - x*A(x) - x^3*A''(x)).
%F A385762 a(0) = 1; a(n) = Sum_{k=0..n-1} (1 - k + k^2) * a(k) * a(n-1-k).
%t A385762 terms = 19; A[_] = 0; Do[A[x_] = 1/(1-x*A[x]-x^3*A''[x]) + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* _Stefano Spezia_, Jul 09 2025 *)
%o A385762 (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, i-1, (1+sum(k=1, 2, stirling(2, k, 1)*j^k))*v[j+1]*v[i-j])); v;
%Y A385762 Cf. A000108, A088716, A385763, A385764, A385765.
%K A385762 nonn
%O A385762 0,3
%A A385762 _Seiichi Manyama_, Jul 09 2025