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 A385698 #7 Jul 07 2025 10:21:01
%S A385698 1,1,1,4,29,256,1501,28715,266001,4590064,99387041,2223185152,
%T A385698 30919119661,1183047504809,21297988134879,656259407452756,
%U A385698 23786602263322385,856920025214144512,18903506095173283273,1086514755640058121323,29116796997476903252841
%N A385698 E.g.f. A(x) satisfies A(x) = exp( x*(A(x) + A(-x))*(A(x) + A(w*x) + A(w^2*x))/6 ), where w = exp(2*Pi*i/3).
%F A385698 a(0) = 1; a(n) = (n-1)! * Sum_{i, j, k>=0 and i+2*j+3*k=n-1} (n-i) * a(i) * a(2*j) * a(3*k)/(i! * (2*j)! * (3*k)!).
%t A385698 terms = 21; w = Exp[2*Pi*I/3]; A[_] = 0; Do[A[x_] = Exp[x*(A[x] + A[-x])*(A[x] + A[w*x] + A[w^2*x])/6 ] + O[x]^terms // Normal, terms]; CoefficientList[A[x], x]Range[0,terms-1]!//Simplify (* _Stefano Spezia_, Jul 07 2025 *)
%Y A385698 Cf. A385699.
%K A385698 nonn
%O A385698 0,4
%A A385698 _Seiichi Manyama_, Jul 07 2025