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 A385764 #12 Jul 09 2025 10:14:21
%S A385764 1,1,2,5,14,378,46500,16879869,14229776750,23948731244678,
%T A385764 72492823741526156,365581334105823084634,2896500982661242290253612,
%U A385764 34419121542689992919239814260,590735385934420874267059790772360,14193599152271246770955912922939691797,465024889616667096875210999651863472880846
%N A385764 G.f. A(x) satisfies A(x) = 1/(1 - x*A(x) - x^5*A''''(x)).
%F A385764 a(0) = 1; a(n) = Sum_{k=0..n-1} (1 - 6*k + 11*k^2 - 6*k^3 + k^4) * a(k) * a(n-1-k).
%t A385764 terms = 17; A[_] = 0; Do[A[x_] = 1/(1-x*A[x]-x^5*A''''[x]) + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* _Stefano Spezia_, Jul 09 2025 *)
%o A385764 (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, 4, stirling(4, k, 1)*j^k))*v[j+1]*v[i-j])); v;
%Y A385764 Cf. A000108, A088716, A385762, A385763, A385765.
%K A385764 nonn
%O A385764 0,3
%A A385764 _Seiichi Manyama_, Jul 09 2025