OFFSET
1,3
COMMENTS
Compare to g.f. C(x) of the Catalan numbers: C(x - x*C(x) + x*C(x)^2) = x.
EXAMPLE
G.f.: A(x) = x + x^2 + 4*x^3 + 21*x^4 + 134*x^5 + 968*x^6 + 7662*x^7 +...
Related expansions.
A(x)^2 = x^2 + 2*x^3 + 9*x^4 + 50*x^5 + 326*x^6 + 2372*x^7 + 18773*x^8 +...
A(x) + A(x)^2 = x + 2*x^2 + 6*x^3 + 30*x^4 + 184*x^5 + 1294*x^6 +...
where the series reversion of A(x) begins:
x-x*A(x)-x*A(x)^2 = x - x^2 - 2*x^3 - 6*x^4 - 30*x^5 - 184*x^6 - 1294*x^7 - 10034*x^8 +...
PROG
(PARI) {a(n)=local(X=x+x*O(x^n), A=X); for(i=1, n, A=serreverse(X*(1-A-A^2))); polcoeff(A, n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Sep 18 2011
STATUS
approved