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 A385692 #8 Jul 07 2025 10:21:06
%S A385692 1,1,3,16,189,2256,32167,767313,16423185,385872832,13923826371,
%T A385692 431494792224,14162204393053,685135173015801,27831222972658029,
%U A385692 1174037911440510736,71264909409165117009,3582888868151242791360,184756481500401258020443,13494513883839138274687425
%N A385692 E.g.f. A(x) satisfies A(x) = exp( x*A(x)*(A(x) + A(w*x) + A(w^2*x))/3 ), where w = exp(2*Pi*i/3).
%F A385692 a(0) = 1; a(n) = (n-1)! * Sum_{i, j, k>=0 and i+j+3*k=n-1} (n-i) * a(i) * a(j) * a(3*k)/(i! * j! * (3*k)!).
%t A385692 terms = 20; w = Exp[2*Pi*I/3]; A[_] = 0; Do[A[x_] = Exp[x*A[x]*(A[x] + A[w*x] + A[w^2*x])/3 ] + O[x]^terms // Normal, terms]; CoefficientList[A[x], x]Range[0,terms-1]!//Simplify (* _Stefano Spezia_, Jul 07 2025 *)
%Y A385692 Cf. A385690.
%K A385692 nonn
%O A385692 0,3
%A A385692 _Seiichi Manyama_, Jul 07 2025