OFFSET
1,3
COMMENTS
Compare g.f. to: F(x) = x + F( -F(x)^2/(1 - F(x) + F(x)^2) ) when F(x) = x/(1+x).
EXAMPLE
G.f.: A(x) = x + x^2 + 3*x^3 + 11*x^4 + 45*x^5 + 199*x^6 + 925*x^7 +...
Related expansions:
A(x)^2 = x^2 + 2*x^3 + 7*x^4 + 28*x^5 + 121*x^6 + 554*x^7 + 2639*x^8 +...
A(x)^2/(1 - A(x) + A(x)^2) = x^2 + 3*x^3 + 10*x^4 + 39*x^5 + 167*x^6 + 760*x^7 + 3607*x^8 + 88440*x^10 +...
PROG
(PARI) {a(n)=local(A=x+x^2); for(i=1, n, A=x+subst(A, x, A^2/(1-A+A^2+x*O(x^n)))); polcoeff(A, n)}
for(n=1, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jun 08 2012
STATUS
approved