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 A385760 #12 Jul 10 2025 22:40:35
%S A385760 1,2,5,15,51,1412,175067,63725638,53784616915,90573359145678,
%T A385760 274256185472187231,1383348290257488337035,10961652126528967555229301,
%U A385760 130268275255842369871718355444,2235924687457083597476492688851325,53724798520519979444347750309693062183
%N A385760 G.f. A(x) satisfies A(x) = 1/((1 - x) * (1 - x*A(x) - x^5*A''''(x))).
%F A385760 a(n) = 1 + Sum_{k=0..n-1} (1 - 6*k + 11*k^2 - 6*k^3 + k^4) * a(k) * a(n-1-k).
%t A385760 terms = 16; A[_] = 0; Do[A[x_] = 1/((1-x)*(1-x*A[x]-x^5*A''''[x])) + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* _Stefano Spezia_, Jul 09 2025 *)
%o A385760 (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, 4, stirling(4, k, 1)*j^k))*v[j+1]*v[i-j])); v;
%Y A385760 Cf. A321087, A385758, A385759, A385761.
%K A385760 nonn
%O A385760 0,2
%A A385760 _Seiichi Manyama_, Jul 09 2025