A202210 G.f.: A(x) = ( Sum_{n>=0} 3^n*(2*n+1) * x^(n*(n+1)/2) )^(1/3).

1, 3, -9, 60, -360, 2457, -18036, 138429, -1093500, 8833140, -72622224, 605563452, -5108366277, 43512281460, -373690245420, 3232056818511, -28126143258444, 246080268205092, -2163254305208580, 19097478037041840, -169235311045503708, 1504837859547132468

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.

Links

Table of n, a(n) for n=0..21.

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

Cf. A193236.

Sequence in context: A018504 A340389 A140812 * A243425 A018513 A143761

Adjacent sequences: A202207 A202208 A202209 * A202211 A202212 A202213

Keyword

sign

Author

Paul D. Hanna, Dec 14 2011

Status

approved