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 A385687 #18 Jul 07 2025 10:46:56
%S A385687 1,1,1,7,25,341,2161,44115,404209,11010025,132273601,4508793983,
%T A385687 67085545033,2747071330173,48765277295281,2331905267846731,
%U A385687 48106649137922017,2631174441142423505,61862217319644572161,3809106344377237185399,100542158725584301036921
%N A385687 E.g.f. A(x) satisfies A(x) = exp( x*((A(x) + A(-x))/2)^2 ).
%F A385687 E.g.f. A(x) satisfies A(-x) = 1/A(x).
%F A385687 a(0) = 1; a(n) = (n-1)! * Sum_{i, j, k>=0 and i+2*j+2*k=n-1} (n-i) * a(i) * a(2*j) * a(2*k)/(i! * (2*j)! * (2*k)!).
%t A385687 terms = 21; A[_] = 1; Do[A[x_] = Exp[x*((A[x] + A[-x])/2)^2] + O[x]^terms // Normal, terms]; CoefficientList[A[x], x]Range[0,terms-1]! (* _Stefano Spezia_, Jul 07 2025 *)
%Y A385687 Cf. A058014, A385688.
%Y A385687 Cf. A143546, A360987, A385690.
%K A385687 nonn
%O A385687 0,4
%A A385687 _Seiichi Manyama_, Jul 06 2025