OFFSET
1,3
COMMENTS
Compare g.f. to: G(x) = x + G( G(x)^2/(1 + G(x) + G(x)^2) ) when G(x) = x/(1-x).
EXAMPLE
G.f.: A(x) = x + x^2 + 2*x^3 + 5*x^4 + 14*x^5 + 43*x^6 + 140*x^7 + 475*x^8 +...
Related expansions:
A(x)^2 = x^2 + 2*x^3 + 5*x^4 + 14*x^5 + 42*x^6 + 134*x^7 + 447*x^8 +...
A(x)^2/(1 + A(x)^2) = x^2 + 2*x^3 + 4*x^4 + 10*x^5 + 29*x^6 + 92*x^7 + 308*x^8 +...
PROG
(PARI) {a(n)=local(A=x+x^2); for(i=1, n, A=x+subst(A, x, A^2/(1+A^2+x*O(x^n)))); polcoeff(A, n)}
for(n=1, 35, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jun 07 2012
STATUS
approved