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A153305 G.f. satisfies: A(x) = x + 3*x*A(x) + 6*x*A(x)*A(A(x)) + 10*x*A(x)*A(A(x))*A(A(A(x))) +... 0

%I

%S 1,3,15,109,1008,10983,135097,1828425,26777775,419530384,6973851684,

%T 122248585620,2249238083514,43274933036838,868047525689328,

%U 18108325893968859,392039367345646323,8792515088387598651

%N G.f. satisfies: A(x) = x + 3*x*A(x) + 6*x*A(x)*A(A(x)) + 10*x*A(x)*A(A(x))*A(A(A(x))) +...

%F x = A(x) - 3*x*A(A(x)) + 3*x*A(x)*A(A(A(x))) - x*A(x)*A(A(x))*A(A(A(A(x)))).

%F A(x) = x*(1 + 3*A(A(x)))/(1 + 3*x*A(A(A(x))) - x*A(A(x))*A(A(A(A(x))))).

%F A(x) = Series_Reversion[x/(1 + 3*A(x) - 3*x*A(A(x)) + x*A(x)*A(A(A(x))))].

%e G.f.: A(x) = x + 3*x^2 + 15*x^3 + 109*x^4 + 1008*x^5 + 10983*x^6 +...

%e A(A(x)) = x + 6*x^2 + 48*x^3 + 470*x^4 + 5328*x^5 + 67557*x^6 +...

%e A(A(A(x))) = x + 9*x^2 + 99*x^3 + 1245*x^4 + 17280*x^5 + 259362*x^6 +...

%e A(A(A(A(x))) = x + 12*x^2 + 168*x^3 + 2596*x^4 + 43128*x^5 + 759306*x^6 +...

%e A(A(A(A(A(x)))) = x + 15*x^2 + 255*x^3 + 4685*x^4 + 91080*x^5 +...

%o (PARI) {a(n)=local(A=x+x*O(x),B,C);for(i=1,n,B=subst(A,x,A);C=subst(A,x,B); A=serreverse(x/(1+3*A-3*x*B+x*A*C)));polcoeff(A,n)}

%Y Cf. A119736.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Jan 04 2009

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Last modified October 18 18:47 EDT 2021. Contains 348068 sequences. (Running on oeis4.)