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%I #8 Oct 21 2020 12:55:43
%S 1,1,3,20,249,5087,155180,6609730,374548937,27237010543,2471980167855,
%T 273862966795982,36371476538686396,5704018487197135820,
%U 1042929404101002643300,219905097318369791869794,52967138256595856156574553,14453277961440111342752817767
%N G.f. satisfies: A(x) = 1/(1 - x - x*{d/dx x^2*A'(x)/A(x)}).
%H Vaclav Kotesovec, <a href="/A183607/b183607.txt">Table of n, a(n) for n = 0..250</a>
%F G.f.: A(x) = (1/x)*Series_Reversion(x/G(x)) where G(x) = A(x/G(x)) is the g.f. of A183606 and satisfies: [x^(n+1)] G(x)^n = n*(n+1)*{[x^n] G(x)^n} for n>=0.
%F G.f. A(x) satisfies: [x^n] exp( n * (x + x^2*A(x)'/A(x)) ) / A(x) = 0 for n > 0. - _Paul D. Hanna_, Oct 21 2020
%F a(n) ~ c * n! * (n-1)!, where c = 2.0524259870985684724972435... - _Vaclav Kotesovec_, Aug 24 2017
%e G.f.: A(x) = 1 + x + 3*x^2 + 20*x^3 + 249*x^4 + 5087*x^5 + 155180*x^6 +...
%o (PARI) {a(n)=local(A=1+x);for(i=1,n,A=1/(1-x - x*deriv(x^2*A'/(A+x*O(x^n)))));polcoeff(A,n)}
%o for(n=0,31,print1(a(n),", "))
%Y Cf. A183606.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Aug 11 2012
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