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 A385761 #11 Jul 10 2025 22:40:15
%S A385761 1,2,5,15,51,188,23291,16862710,42561503035,286183563337662,
%T A385761 4328240254531111671,130903298544350358627387,
%U A385761 7257802488822060515691899445,689810579878520205782663179307100,106537105206016369903910237449838232525,25594900303804029125790200935921438169789415
%N A385761 G.f. A(x) satisfies A(x) = 1/((1 - x) * (1 - x*A(x) - x^6*A'''''(x))).
%F A385761 a(n) = 1 + 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 A385761 terms = 16; A[_] = 0; Do[A[x_] = 1/((1-x)*(1-x*A[x]-x^6*A'''''[x])) + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* _Stefano Spezia_, Jul 09 2025 *)
%o A385761 (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, 5, stirling(5, k, 1)*j^k))*v[j+1]*v[i-j])); v;
%Y A385761 Cf. A321087, A385758, A385759, A385760.
%K A385761 nonn
%O A385761 0,2
%A A385761 _Seiichi Manyama_, Jul 09 2025