G.f.: A(x) = 1 + x + 2*x^2 + 7*x^3 + 36*x^4 + 235*x^5 + 1792*x^6 +...
Related expansions:
A(x)^2 = 1 + 2*x + 5*x^2 + 18*x^3 + 90*x^4 + 570*x^5 + 4247*x^6 +...
1 - 1/A(x) = x + x^2 + 4*x^3 + 23*x^4 + 161*x^5 + 1286*x^6 + 11321*x^7 +...
A(1-1/A(x)) = 1 + x + 3*x^2 + 15*x^3 + 98*x^4 + 753*x^5 + 6471*x^6 +...
Let F(x) = A(1-1/A(x)), then F(1-1/A(x)) = A(1-1/F(x)):
F(1-1/A(x)) = 1 + x + 4*x^2 + 25*x^3 + 193*x^4 + 1693*x^5 + 16240*x^6 +...
...
Let G(x) be the g.f. of
A213591, then
G(x) satisfies: x = G(x - G(x)^2) and G(x) = A(G(x)^2/x), where:
G(x) = x + x^2 + 4*x^3 + 24*x^4 + 178*x^5 + 1512*x^6 + 14152*x^7 +...
G(x)^2/x = x + 2*x^2 + 9*x^3 + 56*x^4 + 420*x^5 + 3572*x^6 +...
1/(1-G(x)^2/x) = 1 + x + 3*x^2 + 14*x^3 + 85*x^4 + 616*x^5 + 5072*x^6 +...
such that A(x/(1 - G(x)^2/x)) = 1/(1 - G(x)^2/x).
