A030201 Expansion of eta(q^3)*eta(q^21).

0, 1, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0

Offset: 0

Author

N. J. A. Sloane

Keywords

• sign
• mult

Comments

Multiplicative. See A002655 for formula. - Andrew Howroyd, Aug 05 2018

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000
• M. Koike, On McKay's conjecture, Nagoya Math. J., 95 (1984), 85-89.

Crossrefs

Expansion of eta(q^k)*eta(q^(24 - k)): A030199 (k=1), this sequence (k=3), A030213 (k=5), A030214 (k=7), A030215 (k=9), A030216 (k=10), A030217 (k=11).

Cf. A002655.

Programs

Mathematica

q QPochhammer[q^3] QPochhammer[q^21] + O[q]^105 // CoefficientList[#, q]& (* Jean-François Alcover, Sep 06 2019 *)

PARI

seq(n)={concat([0], Vec(eta(x^3 + O(x*x^n)) * eta(x^21 + O(x*x^n))))} \\ Andrew Howroyd, Aug 05 2018

Formula

Expansion of x * Product_{k>=1} (1 - x^(3*k)) * (1 - x^(21*k)). - Seiichi Manyama, Oct 18 2016

a(3*n + 1) = A002655(n), a(3*n) = a(3*n + 2) = 0. - Andrew Howroyd, Aug 05 2018