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 A385688 #16 Jul 07 2025 10:46:46
%S A385688 1,1,1,10,37,736,4861,145552,1392553,55772416,700205401,35139710464,
%T A385688 546584937229,32977620613120,612127803448981,43150087404292096,
%U A385688 930914421449463505,75083676142358560768,1846230024226716759601,167681514857730519728128,4629062510444281987051381
%N A385688 E.g.f. A(x) satisfies A(x) = exp( x*((A(x) + A(-x))/2)^3 ).
%F A385688 E.g.f. A(x) satisfies A(-x) = 1/A(x).
%F A385688 a(0) = 1; a(n) = (n-1)! * Sum_{i, j, k, l>=0 and i+2*j+2*k+2*l=n-1} (n-i) * a(i) * a(2*j) * a(2*k) * a(2*l)/(i! * (2*j)! * (2*k)! * (2*l)!).
%t A385688 terms = 21; A[_] = 1; Do[A[x_] = Exp[x*((A[x] + A[-x])/2)^3] + O[x]^terms // Normal, terms]; CoefficientList[A[x], x]Range[0,terms-1]! (* _Stefano Spezia_, Jul 07 2025 *)
%Y A385688 Cf. A058014, A385687.
%Y A385688 Cf. A143547, A360988.
%K A385688 nonn
%O A385688 0,4
%A A385688 _Seiichi Manyama_, Jul 06 2025