cp's OEIS Frontend

A168448 G.f. satisfies: A(x/A(x)^2) = C(x) where C(x) = 1 + x*C(x)^2 is the g.f. of the Catalan numbers (A000108).

%I A168448 #8 Jan 08 2014 16:49:03
%S A168448 1,1,4,26,226,2395,29278,398499,5899534,93507783,1569405110,
%T A168448 27672405800,509622262860,9759305238932,193673399146066,
%U A168448 3972141366536794,84010899306559470,1829057795368804875,40931310532585505770,940322157062673670051,22152626055397162566438
%N A168448 G.f. satisfies: A(x/A(x)^2) = C(x) where C(x) = 1 + x*C(x)^2 is the g.f. of the Catalan numbers (A000108).
%F A168448 G.f. satisfies: A(x) = 1 + A(x)^2*Series_Reversion[x/A(x)^2].
%F A168448 G.f. satisfies: A( (x-x^2)/A(x-x^2)^2 ) = 1/(1-x).
%F A168448 G.f. satisfies: A( (x/(1+x)^2)/A(x/(1+x)^2)^2 ) = 1 + x.
%e A168448 G.f.: A(x) = 1 + x + 4*x^2 + 26*x^3 + 226*x^4 + 2395*x^5 +...
%e A168448 A(x/A(x)^2) = 1 + x + 2*x^2 + 5*x^3 + 14*x^4 + 42*x^5 + 132*x^6 +...
%o A168448 (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, x, serreverse(x/(A+x*O(x^n))^2))); polcoeff(A, n)}
%o A168448 (PARI) {a(n)=local(A=1+x);for(i=1,n,A=1+A^2*serreverse(x/(A+x*O(x^n))^2)); polcoeff(A,n)}
%o A168448 for(n=0,25,print1(a(n),", "))
%Y A168448 Cf. A154677, A168449.
%K A168448 nonn
%O A168448 0,3
%A A168448 _Paul D. Hanna_, Dec 06 2009