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G.f. satisfies: A(x) = B(x*A(x)), where B(x) is the g.f. of A184506.
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%I #3 Dec 22 2012 18:36:48

%S 1,1,1,3,6,33,79,661,1564,19357,39568,751741,1134328,36687892,

%T 30140408,2174316050,65676634,152761870350,-126456152854,

%U 12495122715428,-21554431449186,1173014849466128,-3099148178903788,124924998253897302,-445406039525657880

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

%C G.f. B(x) of A184506 satisfies: B(x) = 1 + x*A(x)*F(x) where F(x) = B(x/F(x)) = A(x/F(x)^2) is the g.f. of A184507 and A(x) is the g.f. of this sequence.

%e G.f.: A(x) = 1 + x + x^2 + 3*x^3 + 6*x^4 + 33*x^5 + 79*x^6 + 661*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) = F(x*A(x)^2) where F(x) = A(x/F(x)^2) is the g.f. of A184507:

%e F(x) = 1 + x - x^2 + 4*x^3 - 16*x^4 + 86*x^5 - 482*x^6 + 3074*x^7 +...

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

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

%Y Cf. A184506, A184507.

%K sign

%O 0,4

%A _Paul D. Hanna_, Dec 22 2012