OFFSET
0,3
FORMULA
G.f. satisfies: A(x) = 1 + x*A(A(x) - 1)/A(1 - A(x)).
EXAMPLE
G.f.: A(x) = 1 + x + 2*x^2 + 6*x^3 + 30*x^4 + 170*x^5 + 1242*x^6 +...
Related expansions.
x*A(-x)/A(x) = x - 2*x^2 + 2*x^3 - 10*x^4 + 18*x^5 - 290*x^6 + 594*x^7 +...
A(A(x)-1) = 1 + x + 4*x^2 + 20*x^3 + 128*x^4 + 928*x^5 + 7636*x^6 +...
A(1-A(x)) = 1 - x - 4*x^3 - 4*x^4 - 112*x^5 - 288*x^6 - 6436*x^7 +...
PROG
(PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+serreverse(x*subst(A, x, -x)/(A+x*O(x^n)))); polcoeff(A, n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Oct 04 2011
STATUS
approved