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G.f. satisfies: A(x) = B(x/A(x)), where B(x) is the g.f. of A184509.
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%I #6 Mar 30 2012 18:37:25

%S 1,1,1,1,4,22,103,565,3650,24574,174621,1326012,10552612,87581914,

%T 758382533,6820324763,63533751777,612270354128,6092311420096,

%U 62498687197246,660267713966489,7174908370818956,80115656652409638,918403116546918196,10799109424669566696

%N G.f. satisfies: A(x) = B(x/A(x)), where B(x) is the g.f. of A184509.

%C The g.f. B(x) of A184509 satisfies B(x) = 1 + x*A(x)*G(x) where G(x) = B(x*G(x)) = A(x*G(x)^2) is the g.f. of A184511 and A(x) = B(x/A(x)) = G(x/A(x)^2) is the g.f. of this sequence.

%e G.f.: A(x) = 1 + x + x^2 + x^3 + 4*x^4 + 22*x^5 + 103*x^6 + 565*x^7 +...

%e G.f.: A(x) = B(x/A(x)) where B(x) = A(x*B(x)) is the g.f. of A184509:

%e B(x) = 1 + x + 2*x^2 + 5*x^3 + 17*x^4 + 78*x^5 + 423*x^6 + 2547*x^7 +...

%e G.f.: A(x) = G(x/A(x)^2) where G(x) = A(x*G(x)^2) is the g.f. of A184511:

%e G(x) = 1 + x + 3*x^2 + 12*x^3 + 58*x^4 + 324*x^5 + 2016*x^6 + 13629*x^7 +...

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

%Y Cf. A184509, A184511.

%K nonn

%O 0,5

%A _Paul D. Hanna_, Dec 30 2011