OFFSET
0,2
FORMULA
G.f. satisfies: A(x) = [1 + A(x)*Series_Reversion(x/A(x))]^3.
G.f. satisfies: A( (x*(1-x)^2)/A(x*(1-x)^2) ) = 1/(1-x)^3.
G.f. satisfies: A( (x/(1+x)^3)/A(x/(1+x)^3) ) = (1 + x)^3.
Self-convolution cube of A168478.
EXAMPLE
G.f.: A(x) = 1 + 3*x + 21*x^2 + 217*x^3 + 2895*x^4 + 46479*x^5 +...
A(x/A(x)) = 1 + 3*x + 12*x^2 + 55*x^3 + 273*x^4 + 1428*x^5 +...+ A001764(n+1)*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^3, 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))))^3); polcoeff(A, n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Dec 06 2009
STATUS
approved