OFFSET
0,2
FORMULA
G.f.: ( (sqrt(1+4*3^4*x^2) + 2*3^2*x)*(sqrt(1+4*3^4*x^2) + 1)/2 )^(1/6).
EXAMPLE
G.f.: A(x) = 1 + 3*x + 18*x^2 - 117*x^3 - 1971*x^4 + 16119*x^5 +...
where
A(x)^3 = 1 + 9*x + 81*x^2 - 6561*x^4 + 1062882*x^6 - 215233605*x^8 +...
A(x)^-3 = 1 - 9*x + 729*x^3 - 118098*x^5 + 23914845*x^7 - 5423886846*x^9 +...
PROG
(PARI) {a(n)=local(A=[1, 3]); for(k=2, n, A=concat(A, 0); if(k%2==1, A[#A]=-Vec(Ser(A)^3)[#A]/3, A[#A]=Vec(Ser(A)^-3)[#A]/3)); A[n+1]}
(PARI) {a(n)=local(X=x+x*O(x^n)); polcoeff(((sqrt(1+4*3^4*X^2) + 2*3^2*x)*(sqrt(1+4*3^4*X^2) + 1)/2 )^(1/6), n)}
CROSSREFS
KEYWORD
sign
AUTHOR
Paul D. Hanna, Oct 06 2011
STATUS
approved