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 A198887 #15 Feb 16 2025 05:38:05
%S A198887 1,1,3,28,269,5056,84247,2400448,57253849,2191568896,68151324491,
%T A198887 3278448139264,125802549088933,7291045162516480,332950230966532831,
%U A198887 22581201334925049856,1196122595530554458033,92934371464549349982208,5602230959364892208231443
%N A198887 E.g.f. satisfies: A(x) = exp(x*A(x)^2*A(-x)).
%C A198887 Limit n->infinity (a(n)/n!)^(1/n) = 1/r = 4.263493124332896881178517333221505445574016761952741537891924..., where r = 0.234549457648408586261093274213550311973... and s = 1.724680091765540585933497362883851976875... are roots of the system of equations s*sqrt((r*s*LambertW(2*r*s))/2) = log(s), s*sqrt((r*s*LambertW(2*r*s))/2)*(4 + 3*LambertW(2*r*s)) = 2*(1 + LambertW(2*r*s)). - _Vaclav Kotesovec_, Jul 16 2014
%H A198887 Vaclav Kotesovec, <a href="/A198887/b198887.txt">Table of n, a(n) for n = 0..240</a>
%F A198887 E.g.f. satisfies x*y^2*sqrt(LambertW(2*x*y)/(2*x*y)) = log(y), where y = A(x). - _Vaclav Kotesovec_, Jul 15 2014
%e A198887 E.g.f.: A(x) = 1 + x + 3*x^2/2! + 28*x^3/3! + 269*x^4/4! + 5056*x^5/5! +...
%e A198887 Related series:
%e A198887 A(x)^2*A(-x) = 1 + x + 7*x^2/2! + 40*x^3/3! + 709*x^4/4! + 8016*x^5/5! +...
%e A198887 log(A(x)) = x + 2*x^2/2! + 21*x^3/3! + 160*x^4/4! + 3545*x^5/5! + 48096*x^6/6! +...
%o A198887 (PARI) {a(n)=local(A=1+x*O(x^n));for(n=0,n,A=exp(x*A^2*subst(A,x,-x)+x*O(x^n)));n!*polcoeff(A,n)}
%Y A198887 Cf. A143600.
%K A198887 nonn
%O A198887 0,3
%A A198887 _Paul D. Hanna_, Oct 30 2011