OFFSET
0,2
COMMENTS
Compare to the q-series identity:
eta(x)^3 = Sum_{n>=0} (-1)^n*(2*n+1) * x^(n*(n+1)/2),
where eta(x) is the Dedekind eta(q) function without the q^(1/24) factor.
FORMULA
Conjecture: a(5*n+4) == 0 (mod 5) (checked up to n = 200). - Peter Bala, Feb 26 2021
EXAMPLE
G.f.: A(x) = 1 + 3*x - 9*x^2 + 60*x^3 - 360*x^4 + 2457*x^5 - 18036*x^6 +...
where
A(x)^3 = 1 + 9*x + 45*x^3 + 189*x^6 + 729*x^10 + 2673*x^15 + 9477*x^21 +...+ 3^n*(2*n+1)*x^(n*(n+1)/2) +...
PROG
(PARI) {a(n)=polcoeff(sum(m=0, sqrtint(2*n+1), 3^m*(2*m+1)*(x)^(m*(m+1)/2)+x*O(x^n))^(1/3), n)}
CROSSREFS
KEYWORD
sign
AUTHOR
Paul D. Hanna, Dec 14 2011
STATUS
approved