OFFSET
0,3
FORMULA
EXAMPLE
G.f.: A(x) = 1 + x + 3*x^2 + 12*x^3 + 58*x^4 + 324*x^5 + 2016*x^6 +...
where A(x) = B(x*A(x)) and B(x) = A(x/B(x)) is the g.f. of A184509:
B(x) = 1 + x + 2*x^2 + 5*x^3 + 17*x^4 + 78*x^5 + 423*x^6 + 2547*x^7 +...
Also, A(x) = F(x*A(x)^2) where F(x) = A(x/F(x)^2) is the g.f. of A184510:
F(x) = 1 + x + x^2 + x^3 + 4*x^4 + 22*x^5 + 103*x^6 + 565*x^7 +...
The product A(x)*F(x) begins:
A(x)*F(x) = 1 + 2*x + 5*x^2 + 17*x^3 + 78*x^4 + 423*x^5 + 2547*x^6 +...
where B(x) = 1 + x*A(x)*F(x).
PROG
(PARI) {a(n)=local(A=1+x+x*O(x^n), F); for(i=1, n, F=(x/serreverse(x*A^2+x*O(x^n)))^(1/2); A=1/x*serreverse(x/(1+x*A*F)) ); polcoeff(A, n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Sep 13 2011
STATUS
approved