OFFSET
0,2
FORMULA
G.f. satisfies: A(x) = [1 + A(x)*Series_Reversion(x/A(x))]^2.
G.f. satisfies: A( (x-x^2)/A(x-x^2) ) = 1/(1-x)^2.
G.f. satisfies: A( (x/(1+x)^2)/A(x/(1+x)^2)^2 ) = (1 + x)^2.
Self-convolution of A168448.
EXAMPLE
G.f.: A(x) = 1 + 2*x + 9*x^2 + 60*x^3 + 520*x^4 + 5450*x^5 +...
A(x/A(x)) = 1 + 2*x + 5*x^2 + 14*x^3 + 42*x^4 + 132*x^5 + 429*x^6 +...
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^2, 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*serreverse(x/(A+x*O(x^n))))^2); polcoeff(A, n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Dec 06 2009
STATUS
approved