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 A385765 #12 Jul 09 2025 10:14:11
%S A385765 1,1,2,5,14,42,5172,3739389,9434483630,63428037194102,
%T A385765 959222215928392076,29009757539769286481866,
%U A385765 1608387988236777669667251772,152866019594999736359695792369300,23609086665918990295149462904374925800,5671917808033245221993631555503554148332485
%N A385765 G.f. A(x) satisfies A(x) = 1/(1 - x*A(x) - x^6*A'''''(x)).
%F A385765 a(0) = 1; a(n) = Sum_{k=0..n-1} (1 + 24*k - 50*k^2 + 35*k^3 - 10*k^4 + k^5) * a(k) * a(n-1-k).
%t A385765 terms = 16; A[_] = 0; Do[A[x_] = 1/(1-x*A[x]-x^6*A'''''[x]) + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* _Stefano Spezia_, Jul 09 2025 *)
%o A385765 (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, 5, stirling(5, k, 1)*j^k))*v[j+1]*v[i-j])); v;
%Y A385765 Cf. A000108, A088716, A385762, A385763, A385764.
%Y A385765 Cf. A385761.
%K A385765 nonn
%O A385765 0,3
%A A385765 _Seiichi Manyama_, Jul 09 2025