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 A214764 G.f. satisfies: A(x) = 1/A(-x*A(x)^4). 8

%I

%S 1,2,10,60,390,2660,18772,138984,1107686,9576100,87944188,830857464,

%T 7876505340,73967614584,685644645896,6289047266480,57465415636166,

%U 528315307772004,4947263762389484,47785581838822232,480797992896880788,5058812497153271912

%N G.f. satisfies: A(x) = 1/A(-x*A(x)^4).

%C Compare to: W(x) = 1/W(-x*W(x)^4) when W(x) = Sum_{n>=0} (2*n+1)^(n-1)*x^n/n!.

%C Compare to: B(x) = 1/B(-x*B(x)^4) when B(x) = 1/(1-8*x)^(1/4) = g.f. of A004981.

%C An infinite number of functions G(x) satisfy (*) G(x) = 1/G(-x*G(x)^4); for example, (*) is satisfied by G(x) = W(m*x), where W(x) = Sum_{n>=0} (2*n+1)^(n-1)*x^n/n!.

%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)^4))/2 starting at G_0(x) = 1+2*x.

%e G.f.: A(x) = 1 + 2*x + 10*x^2 + 60*x^3 + 390*x^4 + 2660*x^5 + 18772*x^6 +...

%e A(x)^4 = 1 + 8*x + 64*x^2 + 512*x^3 + 4096*x^4 + 32800*x^5 + 263168*x^6 +...

%o (PARI) {a(n)=local(A=1+2*x);for(i=0,n,A=(A+1/subst(A,x,-x*A^4+x*O(x^n)))/2);polcoeff(A,n)}

%o for(n=0,31,print1(a(n),", "))

%Y Cf. A214761, A214762, A214763, A214765, A214766, A214767, A214768, A214769.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Jul 29 2012

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Last modified December 2 09:52 EST 2020. Contains 338876 sequences. (Running on oeis4.)