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 A168449 G.f. satisfies: A(x/A(x)) = C(x)^2 where C(x) = 1 + x*C(x)^2 is the g.f. of the Catalan numbers (A000108). 3

%I #2 Mar 30 2012 18:37:20

%S 1,2,9,60,520,5450,65830,886466,13005906,204607622,3412713687,

%T 59858823020,1097439583778,20934702108924,414042879930671,

%U 8466407067384676,178587080601453990,3878812336463745962

%N G.f. satisfies: A(x/A(x)) = C(x)^2 where C(x) = 1 + x*C(x)^2 is the g.f. of the Catalan numbers (A000108).

%F G.f. satisfies: A(x) = [1 + A(x)*Series_Reversion(x/A(x))]^2.

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

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

%F Self-convolution of A168448.

%e G.f.: A(x) = 1 + 2*x + 9*x^2 + 60*x^3 + 520*x^4 + 5450*x^5 +...

%e A(x/A(x)) = 1 + 2*x + 5*x^2 + 14*x^3 + 42*x^4 + 132*x^5 + 429*x^6 +...

%o (PARI) {a(n)=local(A=1+x, F=sum(k=0, n, binomial(2*k+1, k)/(2*k+1)*x^k)+x*O(x^n)); for(i=0, n, A=subst(F^2, x, serreverse(x/(A+x*O(x^n))))); polcoeff(A, n)}

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

%Y Cf. A154677, A168448, A168479 (variant).

%K nonn

%O 0,2

%A _Paul D. Hanna_, Dec 06 2009

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Last modified October 4 23:44 EDT 2023. Contains 365888 sequences. (Running on oeis4.)