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 A385759 #12 Jul 10 2025 22:40:41
%S A385759 1,2,5,15,141,3932,251717,31216948,6680698525,2271470142438,
%T A385759 1153913665217481,835435792656039975,830424340158140342961,
%U A385759 1099482665756962845820704,1891111018270919721409143729,4137752010118540256190073466415,11312615890237585633045672755792789
%N A385759 G.f. A(x) satisfies A(x) = 1/((1 - x) * (1 - x*A(x) - x^4*A'''(x))).
%F A385759 a(n) = 1 + Sum_{k=0..n-1} (1 + 2*k - 3*k^2 + k^3) * a(k) * a(n-1-k).
%t A385759 terms = 17; A[_] = 0; Do[A[x_] = 1/((1-x)*(1-x*A[x]-x^4*A'''[x])) + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* _Stefano Spezia_, Jul 09 2025 *)
%o A385759 (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, 3, stirling(3, k, 1)*j^k))*v[j+1]*v[i-j])); v;
%Y A385759 Cf. A321087, A385758, A385760, A385761.
%K A385759 nonn
%O A385759 0,2
%A A385759 _Seiichi Manyama_, Jul 09 2025