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 A385691 #14 Jul 07 2025 10:21:30
%S A385691 1,1,1,1,5,21,61,568,4257,20917,286451,3099141,21555865,390273898,
%T A385691 5524889553,49790422501,1121734897937,19631020478229,217441607213557,
%U A385691 5862333450708460,122222268766006641,1606671304363320805,50443794604147639487,1220712011020970521461
%N A385691 E.g.f. A(x) satisfies A(x) = exp( x*(A(x) + A(w*x) + A(w^2*x))/3 ), where w = exp(2*Pi*i/3).
%F A385691 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/3)} (3*k+1) * binomial(n-1,3*k) * a(3*k) * a(n-1-3*k).
%t A385691 terms = 24; w = Exp[2*Pi*I/3]; A[_] = 1; Do[A[x_] = Exp[x*(A[x] + A[w*x] + A[w^2*x])/3] + O[x]^terms // Normal, terms]; Simplify[CoefficientList[A[x], x]Range[0,terms-1]!] (* _Stefano Spezia_, Jul 07 2025 *)
%Y A385691 Cf. A058014, A124753.
%K A385691 nonn
%O A385691 0,5
%A A385691 _Seiichi Manyama_, Jul 07 2025