A030220 Expansion of (eta(q^3)*eta(q^5))^3 in powers of q.

1, 0, 0, -3, 0, -3, 0, 0, 9, 5, 0, 0, 0, 0, -15, 5, 0, 0, -22, 0, 0, 0, 0, 21, 25, 0, 0, 0, 0, 0, 2, 0, 0, -14, 0, -27, 0, 0, 0, -35, 0, 0, 0, 0, 0, 34, 0, 0, 49, 0, 42, 0, 0, -27, 0, 0, 0, 0, 0, 45, -118, 0, 0, 13, 0, 0, 0, 0, -102, 0, 0, 0, 0, 0, 0, 66, 0, 0, 98, 0, 81, 0, 0, 0, -70, 0, 0, 0, 0, 45, 0, 0, 0, -14

Offset

1,4

Links

Seiichi Manyama, Table of n, a(n) for n = 1..10000

M. Koike, On McKay's conjecture, Nagoya Math. J., 95 (1984), 85-89.

Formula

Euler transform of period 15 sequence [ 0, 0, -3, 0, -3, -3, 0, 0, -3, -3, 0, -3, 0, 0, -6, ...]. - Michael Somos, Jun 14 2007

G.f.: (1/2)* Sum_{u,v} (u*u -4*v*v)* x^(u*u +u*v +4*v*v). - Michael Somos, Jun 14 2007

G.f.: x*(Product_{k>0} (1-x^(3*k))(1-x^(5*k)))^3. - Michael Somos, Jun 14 2007

Example

q - 3*q^4 - 3*q^6 + 9*q^9 + 5*q^10 - 15*q^15 + 5*q^16 - 22*q^19 + 21*q^24 + ...

Mathematica

QP = QPochhammer; s = (QP[q^3]*QP[q^5])^3 + O[q]^100; CoefficientList[s, q] (* Jean-François Alcover, Nov 25 2015 *)

Crossrefs

Sequence in context: A300288 A340555 A094901 * A219240 A349612 A277080

Adjacent sequences: A030217 A030218 A030219 * A030221 A030222 A030223

Keyword

sign

Author

N. J. A. Sloane, Dec 11 1999

Status

approved