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%I #4 Jul 29 2012 14:41:24
%S 1,2,20,220,2280,25920,443744,10057408,215047552,3841564160,
%T 57161584256,757459114112,10427052678656,166827795710208,
%U 2728593278189568,38108069305433088,521570277192555520,14195894062729323520,594582326909611536384,21399757674339677249536
%N G.f. satisfies: A(x) = 1/A(-x*A(x)^9).
%C Compare g.f. to: G(x) = 1/G(-x*G(x)^7) when G(x) = 1 + x*G(x)^5 (A002294).
%C An infinite number of functions G(x) satisfy (*) G(x) = 1/G(-x*G(x)^9); for example, (*) is satisfied by G(x) = F(m*x) = 1 + m*x*F(m*x)^5 for all m, where F(x) is the g.f. of A002294.
%F The g.f. of this sequence is the limit of the recurrence:
%F (*) G_{n+1}(x) = (G_n(x) + 1/G_n(-x*G_n(x)^9))/2 starting at G_0(x) = 1+2*x.
%e G.f.: A(x) = 1 + 2*x + 20*x^2 + 220*x^3 + 2280*x^4 + 25920*x^5 + 443744*x^6 +...
%e A(x)^5 = 1 + 10*x + 140*x^2 + 1980*x^3 + 26680*x^4 + 362432*x^5 + 5617920*x^6 +...
%e A(x)^9 = 1 + 18*x + 324*x^2 + 5532*x^3 + 88776*x^4 + 1386432*x^5 + 22460832*x^6 +...
%o (PARI) {a(n)=local(A=1+2*x);for(i=0,n,A=(A+1/subst(A,x,-x*A^9+x*O(x^n)))/2);polcoeff(A,n)}
%o for(n=0,31,print1(a(n),", "))
%Y Cf. A214761, A214762, A214763, A214764, A214765, A214766, A214767, A214768.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Jul 29 2012
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