%I A143342
%S A143342 1,1,6,40,374,3215,34298,326360,3710278,37289620,440121880,4577214736,
%T A143342 55375589594,589530372890,7258264793564,78597770766160,980423896907046,
%U A143342 10754940952651740,135521929778850952,1501817992511869280
%N A143342 G.f. satisfies: A(x) = 1 + x*A(x)^5/A(-x).
%C A143342 More generally, if A(x) = 1 + x*A(x)^n/A(-x)
%C A143342 then A(x) - x*A(x)^n = 1 + x^2*[A(x)*A(-x)]^(n-1)
%C A143342 so that a bisection of A(x) equals a bisection of A(x)^n.
%F A143342 G.f. satisfies: A(x) - x*A(x)^5 = 1 + x^2*[A(x)*A(-x)]^4.
%e A143342 A bisection of g.f. A(x) equals a bisection of A(x)^5:
%e A143342 A(x) = 1 + x + 6*x^2 + 40*x^3 + 374*x^4 + 3215*x^5 + 34298*x^6 + 326360*x^7 
               +...
%e A143342 A(x)^5 = 1 + 5*x + 40*x^2 + 330*x^3 + 3215*x^4 + 30756*x^5 + 326360*x^6 
               +...
%e A143342 so that A(x) - x*A(x)^5 = 1 + x^2*[A(x)*A(-x)]^4, where
%e A143342 [A(x)*A(-x)]^4 = 1 + 44*x^2 + 3542*x^4 + 358468*x^6 + 40846025*x^8 + 
               +...
%e A143342 A(x)*A(-x) = 1 + 11*x^2 + 704*x^4 + 65054*x^6 + 7062088*x^8 +...
%o A143342 (PARI) {a(n)=local(A=1+x+x*O(x^n));for(i=0,n,A=1+x*A^5/subst(A,x,-x));
               polcoeff(A,n)}
%Y A143342 Cf. A143339, A143340, A143341.
%Y A143342 Sequence in context: A006387 A014481 A000683 this_sequence A084270 A053677 
               A001367
%Y A143342 Adjacent sequences: A143339 A143340 A143341 this_sequence A143343 A143344 
               A143345
%K A143342 nonn
%O A143342 0,3
%A A143342 Paul D. Hanna (pauldhanna(AT)juno.com), Aug 09 2008