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 A168653 G.f. satisfies: A(x*A(x)) = G(x) where G(x) = 1 + x*G(x)^3 is the g.f. of A001764. 0

%I

%S 1,1,2,6,21,82,340,1478,6622,30433,142331,676203,3248579,15776459,

%T 77196573,380849394,1888606247,9430534212,47236684433,238214461960,

%U 1202007809362,6116704517639,30997312336216,159384351652358

%N G.f. satisfies: A(x*A(x)) = G(x) where G(x) = 1 + x*G(x)^3 is the g.f. of A001764.

%F G.f. satisfies: A(x) = 1 + A(x)^3*Series_Reversion(x*A(x)).

%F G.f. satisfies: A( x*(1-x)^2*A(x*(1-x)^2) ) = 1/(1-x).

%F G.f. satisfies: A( (x/(1+x)^3)*A(x/(1+x)^3) ) = 1 + x.

%e G.f.: A(x) = 1 + x + 2*x^2 + 6*x^3 + 21*x^4 + 82*x^5 + 340*x^6 +...

%e A(x*A(x)) = 1 + x + 3*x^2 + 12*x^3 + 55*x^4 + 273*x^5 + 1428*x^6 +...

%o (PARI) {a(n)=local(A=1+x, F=sum(k=0, n, binomial(3*k+1, k)/(3*k+1)*x^k)+x*O(x^n)); for(i=0, n, A=subst(F, x, serreverse(x*(A+x*O(x^n))^1))); polcoeff(A, n)}

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

%Y Cf. A154677, A168478, A168448, A001764.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Dec 06 2009

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Last modified June 20 15:00 EDT 2021. Contains 345165 sequences. (Running on oeis4.)