OFFSET
0,3
FORMULA
G.f. satisfies: A(x) = 1 + A(x)^3*Series_Reversion[x/A(x)^3].
G.f. satisfies: A( (x*(1-x)^2)/A(x*(1-x)^2)^3 ) = 1/(1-x).
G.f. satisfies: A( (x/(1+x)^3)/A(x/(1+x)^3)^3 ) = 1 + x.
EXAMPLE
G.f.: A(x) = 1 + x + 6*x^2 + 60*x^3 + 803*x^4 + 13071*x^5 +...
A(x/A(x)^3) = 1 + x + 3*x^2 + 12*x^3 + 55*x^4 + 273*x^5 + 1428*x^6 +...+ A001764(n)*x^n +...
PROG
(PARI) {a(n)=local(A=1+x, F=sum(k=0, n, binomial(3*k+1, k)/(3*k+1)*x^k)+x*O(x^n)); for(i=0, n, A=subst(F, x, serreverse(x/(A+x*O(x^n))^3))); polcoeff(A, n)}
(PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+A^3*serreverse(x/(A+x*O(x^n))^3)); polcoeff(A, n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Dec 06 2009
STATUS
approved