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 A385763 #12 Jul 09 2025 10:14:32
%S A385763 1,1,2,5,44,1188,74880,9211479,1962123260,665169218468,
%T A385763 337242780292376,243827199998597254,242120748323922920272,
%U A385763 320325994582940359050400,550640627320172764415124000,1204251372776149567847238889047,3291219553094816112273747054673476
%N A385763 G.f. A(x) satisfies A(x) = 1/(1 - x*A(x) - x^4*A'''(x)).
%F A385763 a(0) = 1; a(n) = Sum_{k=0..n-1} (1 + 2*k - 3*k^2 + k^3) * a(k) * a(n-1-k).
%t A385763 terms = 17; A[_] = 0; Do[A[x_] = 1/(1-x*A[x]-x^4*A'''[x]) + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* _Stefano Spezia_, Jul 09 2025 *)
%o A385763 (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, 3, stirling(3, k, 1)*j^k))*v[j+1]*v[i-j])); v;
%Y A385763 Cf. A000108, A088716, A385762, A385764, A385765.
%K A385763 nonn
%O A385763 0,3
%A A385763 _Seiichi Manyama_, Jul 09 2025