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 A385845 #10 Jul 10 2025 10:58:42
%S A385845 1,1,1,1,7,175,10675,1291675,272543461,91847148373,46382810082589,
%T A385845 33442006088446669,33141028037446336195,43779298038683546954491,
%U A385845 75169054733013247990186039,164244384592052866115015051119,448551414321306169623754824645385
%N A385845 G.f. A(x) satisfies A(x) = 1/((1 - x) * (1 - x^4*A'''(x))).
%F A385845 a(n) = 1 + Sum_{k=0..n-1} (2*k - 3*k^2 + k^3) * a(k) * a(n-1-k).
%t A385845 terms = 17; A[_] = 0; Do[A[x_] = 1/((1 - x) * (1 - x^4*A'''[x])) + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* _Stefano Spezia_, Jul 10 2025 *)
%o A385845 (PARI) a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=1+sum(j=0, i-1, sum(k=1, 3, stirling(3, k, 1)*j^k)*v[j+1]*v[i-j])); v;
%Y A385845 Cf. A143917, A385844, A385846.
%Y A385845 Cf. A385759.
%K A385845 nonn
%O A385845 0,5
%A A385845 _Seiichi Manyama_, Jul 09 2025