%I A143134
%S A143134 1,2,12,112,1440,23552,467712,10926592,293544960,8914583552,
%T A143134 301957742592,11285975498752,461367611228160,20477098870833152,
%U A143134 980591931131953152,50393637174029320192,2766350676943951626240
%N A143134 E.g.f. satisfies: A(x) = x + sin( A(x) )^2 with A(0)=0.
%C A143134 Radius of convergence of A(x) is r = Pi/4 - 1/2, with A(r) = Pi/4.
%F A143134 E.g.f.: A(x) = Series_Reversion( x - sin(x)^2 ).
%F A143134 E.g.f. derivative: A'(x) = 1/(1 - 2*sqrt(A(x)-x)*sqrt(1+x-A(x))); thus 
               A'(x) = 1/(1 - sin(2*A(x))).
%e A143134 A(x) = x + 2*x^2/2! + 12*x^3/3! + 112*x^4/4! + 1440*x^5/5! +...
%e A143134 sin(A(x)) = G(x) is the e.g.f. of A143135:
%e A143134 G(x) = x + 2*x^2/2! + 11*x^3/3! + 100*x^4/4! + 1261*x^5/5! +...
%e A143134 G(x)^2 = 2*x^2/2! + 12*x^3/3! + 112*x^4/4! + 1440*x^5/5! +...
%o A143134 (PARI) {a(n)=local(A=x);for(i=0,n,A=x + sin(A)^2);n!*polcoeff(A,n)}
%o A143134 (PARI) {a(n)=n!*polcoeff(serreverse(x-sin(x+x*O(x^n))^2),n)}
%Y A143134 Cf. A143135, A143136.
%Y A143134 Sequence in context: A047855 A009232 A124213 this_sequence A091481 A053312 
               A091854
%Y A143134 Adjacent sequences: A143131 A143132 A143133 this_sequence A143135 A143136 
               A143137
%K A143134 nonn
%O A143134 1,2
%A A143134 Paul D. Hanna (pauldhanna(AT)juno.com), Jul 27 2008