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A217989 G.f. satisfies: A(x) = 1+x + x^2*A'(x)*A(x)^2.

%I A217989 #20 Feb 22 2014 06:38:42
%S A217989 1,1,1,4,19,116,835,6890,63826,654552,7354893,89830770,1184915556,
%T A217989 16788863356,254342837905,4103256660048,70241858430220,
%U A217989 1271839899568064,24287699718766932,487891841580468294,10285169201486942788,227042177973572054900
%N A217989 G.f. satisfies: A(x) = 1+x + x^2*A'(x)*A(x)^2.
%H A217989 Vaclav Kotesovec, <a href="/A217989/b217989.txt">Table of n, a(n) for n = 0..445</a>
%F A217989 a(n) ~ c * n! * n, where c = 0.21362630601338471861707529847387... - _Vaclav Kotesovec_, Feb 22 2014
%e A217989 G.f.: A(x) = 1 + x + x^2 + 4*x^3 + 19*x^4 + 116*x^5 + 835*x^6 + 6890*x^7 +...
%e A217989 Related expansions:
%e A217989 A'(x) = 1 + 2*x + 12*x^2 + 76*x^3 + 580*x^4 + 5010*x^5 + 48230*x^6 +...
%e A217989 A(x)^2 = 1 + 2*x + 3*x^2 + 10*x^3 + 47*x^4 + 278*x^5 + 1956*x^6 + 15834*x^7 +...
%o A217989 (PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+x+x^2*A'*(A^2+x*O(x^n))); polcoeff(A, n)}
%o A217989 for(n=0, 30, print1(a(n), ", "))
%Y A217989 Cf. A143916, A218223.
%K A217989 nonn
%O A217989 0,4
%A A217989 _Paul D. Hanna_, Oct 23 2012