OFFSET
0,3
LINKS
Paul D. Hanna, Table of n, a(n) for n = 0..200
FORMULA
G.f. satisfies: A( (x-x^2)/A(x-x^2) ) = 1/(1-x).
G.f. satisfies: A( (x/(1+x)^2)/A(x/(1+x)^2) ) = 1 + x.
G.f. satisfies: A(x) = 1 + A(x)^2*Series_Reversion(x/A(x)). - Paul D. Hanna, Dec 06 2009
EXAMPLE
G.f.: A(x) = 1 + x + 3*x^2 + 13*x^3 + 70*x^4 + 440*x^5 + ... where
A(x/A(x)) = 1 + x + 2*x^2 + 5*x^3 + 14*x^4 + 42*x^5 + 132*x^6 + ...
x/A(x) = x - x^2 - 2*x^3 - 8*x^4 - 43*x^5 - 277*x^6 - 2026*x^7 - ...
PROG
(PARI) {a(n)=local(A=1+x, F=sum(k=0, n, binomial(2*k+1, k)/(2*k+1)*x^k)+x*O(x^n)); for(i=0, n, A=subst(F, x, serreverse(x/(A+x*O(x^n))))); polcoeff(A, n)}
(PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+A^2*serreverse(x/(A+x*O(x^n)))); polcoeff(A, n)} \\ Paul D. Hanna, Dec 06 2009
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jan 14 2009
STATUS
approved