OFFSET
1,2
COMMENTS
The half-iteration of the g.f. equals an integer series (A213009).
LINKS
Paul D. Hanna, Table of n, a(n) for n = 1..256
FORMULA
G.f. satisfies: A(x) = x/G(x) - 1 - G(x) where A(G(x)) = x.
EXAMPLE
G.f.: A(x) = x + 2*x^2 + 4*x^3 + 16*x^4 + 80*x^5 + 480*x^6 + 3296*x^7 +...
where
A(A(x)) = x + 4*x^2 + 16*x^3 + 80*x^4 + 480*x^5 + 3296*x^6 +...
Related expansions.
Let B(B(x)) = A(x), then B(x) is an integer series:
B(x) = x + x^2 + x^3 + 5*x^4 + 21*x^5 + 125*x^6 + 825*x^7 + 6133*x^8 +...
where the coefficients of B(x) are congruent to 1 modulo 4.
PROG
(PARI) {a(n)=local(A=x+2*x^2); for(i=1, n, A=x+x^2+x*subst(A, x, A+x*O(x^n))); polcoeff(A, n)}
for(n=1, 31, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jun 01 2012
STATUS
approved