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%I #8 Jul 10 2015 03:20:00
%S 1,1,1,2,9,66,646,7760,109585,1771810,32211854,649833996,14399543754,
%T 347618918364,9080945744920,255239884317292,7680997048377377,
%U 246417820289930866,8395878803694101510,302786064773642534220,11523127939987785101646,461518291638811484923036
%N G.f. satisfies: A(x) = 1+x + x^2 * A'(x)^2 / A(x)^2.
%H Vaclav Kotesovec, <a href="/A259607/b259607.txt">Table of n, a(n) for n = 0..350</a>
%F a(n) ~ c * 2^n * (n-1)!, where c = 0.09202081821632249728460... . - _Vaclav Kotesovec_, Jul 10 2015
%e G.f.: A(x) = 1 + x + x^2 + 2*x^3 + 9*x^4 + 66*x^5 + 646*x^6 + 7760*x^7 +...
%e The logarithmic derivative begins:
%e A'(x)/A(x) = 1 + x + 4*x^2 + 29*x^3 + 286*x^4 + 3478*x^5 + 49750*x^6 + 813949*x^7 +...+ A182356(n)*x^n +...
%e where
%e A'(x)^2/A(x)^2 = 1 + 2*x + 9*x^2 + 66*x^3 + 646*x^4 + 7760*x^5 +...
%o (PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+x + x^2*(A')^2/A^2 +x*O(x^n)); polcoeff(A, n)}
%o for(n=0, 30, print1(a(n), ", "))
%Y Cf. A182356.
%K nonn
%O 0,4
%A _Paul D. Hanna_, Jul 05 2015
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