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 A385758 #13 Jul 10 2025 22:40:46
%S A385758 1,2,5,25,241,3850,92699,3159424,145529893,8737971990,664337673319,
%T A385758 62461188300465,7121505696653881,968606284138975286,
%U A385758 154985833403909522361,28828521246104115576631,6169483384435711859804021,1505386674395483103372685258,415493606617772745031305469471
%N A385758 G.f. A(x) satisfies A(x) = 1/((1 - x) * (1 - x*A(x) - x^3*A''(x))).
%F A385758 a(n) = 1 + Sum_{k=0..n-1} (1 - k + k^2) * a(k) * a(n-1-k).
%t A385758 terms = 19; A[_] = 0; Do[A[x_] = 1/((1-x)*(1-x*A[x]-x^3*A''[x])) + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* _Stefano Spezia_, Jul 09 2025 *)
%o A385758 (PARI) a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=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 A385758 Cf. A321087, A385759, A385760, A385761.
%Y A385758 Cf. A385762.
%K A385758 nonn
%O A385758 0,2
%A A385758 _Seiichi Manyama_, Jul 09 2025