A184507 - OEIS

%I #3 Dec 22 2012 18:35:36

%S 1,1,-1,4,-16,86,-482,3074,-20478,147227,-1101843,8702605,-71285202,

%T 609348589,-5385150192,49346937185,-466332024088,4550830295128,

%U -45705121373663,472675376094619,-5022099348895724,54826872973024796,-613998703071634703,7052884860025205276

%N  G.f. satisfies: A(x) = B(x/A(x)), where B(x) is the g.f. of A184506.

%C  The g.f. B(x) of A184506 satisfies B(x) = 1 + x*G(x)/A(x) where G(x) = B(x*G(x)) = A(x*G(x)^2) is the g.f. of A184508 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 + 4*x^3 - 16*x^4 + 86*x^5 - 482*x^6 + 3074*x^7 +...

%e Related expansions.

%e A(x) = B(x/A(x)) where B(x) = A(x*B(x)) is the g.f. of A184506:

%e B(x) = 1 + x + 2*x^3 - 3*x^4 + 27*x^5 - 91*x^6 + 723*x^7 -+...

%e Also, A(x) = G(x/A(x)^2) where  G(x) = A(x*G(x)^2) is the g.f. of A184508:

%e G(x) = 1 + x + x^2 + 3*x^3 + 6*x^4 + 33*x^5 + 79*x^6 + 661*x^7 +...

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

%o for(n=0,30,print1(a(n),", "))

%Y  Cf. A184506, A184508.

%K sign

%O 0,4

%A _Paul D. Hanna_, Dec 22 2012