A122792 Expansion of eta(q^2)^2/(eta(q)eta(q^3)) in powers of q.

1, 1, 0, 2, 1, 0, 4, 2, 0, 6, 4, 0, 10, 6, 0, 16, 9, 0, 24, 14, 0, 36, 20, 0, 52, 29, 0, 74, 42, 0, 104, 58, 0, 144, 80, 0, 198, 110, 0, 268, 148, 0, 360, 198, 0, 480, 264, 0, 634, 347, 0, 832, 454, 0, 1084, 592, 0, 1404, 764, 0, 1808, 982, 0, 2316, 1257, 0, 2952, 1598, 0

Offset: 0

Author

Michael Somos, Sep 11 2006

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000

Crossrefs

A098151(n)=a(3n). A097197(n)=a(3n+1).

Cf. A293306.

Programs

Mathematica

QP = QPochhammer; s = QP[q^2]^2/(QP[q]*QP[q^3]) + O[q]^70; CoefficientList[s, q] (* Jean-François Alcover, Nov 25 2015 *)

PARI

{a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( eta(x^2+A)^2/eta(x+A)/eta(x^3+A), n))}

Formula

Euler transform of period 6 sequence [ 1, -1, 2, -1, 1, 0, ...].

G.f.: Product_{k>0} (1-x^k)^2/(1+x^k+x^(2k)). a(3n+2)=0.

G.f.: Product_{i>0} 1/(1 + Sum_{j>0} (-1)^j*j*q^(j*i)). - Seiichi Manyama, Oct 08 2017