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 A385690 #11 Jul 07 2025 10:46:40
%S A385690 1,1,3,25,233,3901,62707,1591493,36539953,1246111705,37259797091,
%T A385690 1597211237425,58891746904729,3041999861503253,133421178853319827,
%U A385690 8066042741507516701,410229480337750129889,28415048957473232282161,1644249408980809155863491
%N A385690 E.g.f. A(x) satisfies A(x) = exp( x*A(x)*(A(x) + A(-x))/2 ).
%F A385690 a(0) = 1; a(n) = (n-1)! * Sum_{i, j, k>=0 and i+j+2*k=n-1} (n-i) * a(i) * a(j) * a(2*k)/(i! * j! * (2*k)!).
%t A385690 terms = 19; A[_] = 1; Do[A[x_] = Exp[x*A[x]*(A[x] + A[-x])/2] + O[x]^terms // Normal, terms]; CoefficientList[A[x], x]Range[0,terms-1]! (* _Stefano Spezia_, Jul 07 2025 *)
%Y A385690 Cf. A217138, A385687, A385692.
%K A385690 nonn
%O A385690 0,3
%A A385690 _Seiichi Manyama_, Jul 07 2025