OFFSET
3,2
EXAMPLE
G.f.: A(x) = x^3 + 3*x^5 + 12*x^7 + 55*x^9 + 276*x^11 + 1470*x^13 +...
A(x)^(1/3) = x + x^3 + 3*x^5 + 12*x^7 + 56*x^9 + 285*x^11 +...
Related expansions:
A(A(x)) = x^9 + 9*x^11 + 63*x^13 + 411*x^15 + 2619*x^17 + 16569*x^19 +..
A(A(A(x))) = x^27 + 27*x^29 + 432*x^31 + 5364*x^33 + 57267*x^35 +...
A(A(A(A(x)))) = x^81 + 81*x^83 + 3483*x^85 + 105759*x^87 +...
where A(x)^(1/3) = x + A(x) + A(A(x)) + A(A(A(x))) + A(A(A(A(x)))) +...
PROG
(PARI) {a(n)=local(A=x+x^3); for(i=0, n, A=serreverse(x-subst(A, x, x^3+x^2*O(x^(2*n))))); polcoeff(A^3, 2*n-1)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Aug 12 2010
STATUS
approved