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 A385844 #12 Jul 10 2025 10:58:39
%S A385844 1,1,1,3,21,273,5737,177919,7651849,436186313,31842549569,
%T A385844 2897710853939,321648004495773,42779331295225353,6716367934603667145,
%U A385844 1229096733282700520799,259339594018913458094865,62500870590534491566841265,17062742827503910747790541249,5238263128497776755775631825219
%N A385844 G.f. A(x) satisfies A(x) = 1/((1 - x) * (1 - x^3*A''(x))).
%F A385844 a(n) = 1 + Sum_{k=0..n-1} (-k + k^2) * a(k) * a(n-1-k).
%t A385844 terms = 20; A[_] = 0; Do[A[x_] = 1/((1 - x) * (1 - x^3*A''[x])) + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* _Stefano Spezia_, Jul 10 2025 *)
%o A385844 (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, 2, stirling(2, k, 1)*j^k)*v[j+1]*v[i-j])); v;
%Y A385844 Cf. A143917, A385845, A385846.
%Y A385844 Cf. A385758, A385762.
%K A385844 nonn
%O A385844 0,4
%A A385844 _Seiichi Manyama_, Jul 09 2025