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%I #25 Mar 30 2012 18:37:33
%S 1,2,4,12,42,158,618,2498,10360,43832,188420,820608,3613212,16057640,
%T 71933768,324482500,1472604586,6719100254,30804229858,141829955338,
%U 655541387406,3040527731790,14147444737654,66018910398574,308898542610666,1448867831911170
%N G.f. satisfies: A(x) = exp( Sum_{n>=1} (A(x) - (-1)^n)^n * x^n/n ).
%F G.f. satisfies: A(x) = 1/(1-x*A(x)) * exp( Sum_{n>=1} 1/(1 - (-1)^n*x*A(x))^n * x^n/n ).
%F G.f. satisfies: A(x) = sqrt( (1 - (A(x)+1)^2*x^2)/(1 - (A(x)-1)^2*x^2) ) / (1 - (A(x)+1)*x).
%F G.f. satisfies: 0 = -(1+x) - x*A(x) + (1+x)*(1-x)^2*A(x)^2 - x*(1-x)^2*A(x)^3 - x^2*(1+x)*A(x)^4 + x^3*A(x)^5.
%e G.f.: A(x) = 1 + 2*x + 4*x^2 + 12*x^3 + 42*x^4 + 158*x^5 + 618*x^6 +...
%e where
%e log(A(x)) = (A(x) + 1)*x + (A(x) - 1)^2*x^2/2 + (A(x) + 1)^3*x^3/3 + (A(x) - 1)^4*x^4/4 +...
%e log(A(x)*(1-x*A(x))) = 1/(1 + x*A(x))*x + 1/(1 - x*A(x))^2*x^2/2 + 1/(1 + x*A(x))^3*x^3/3 + 1/(1 - x*A(x))^4*x^4/4 +...
%o (PARI) {a(n)=local(A=1+x); for(i=1, n, A=exp(sum(m=1, n, (A-(-1)^m+x*O(x^n))^m*x^m/m))); polcoeff(A, n)}
%Y Cf. A202669, A185385, A202630, A202518, A155200.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Dec 22 2011
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