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

0,4

Links

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

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

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 *)

Prog

(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))}

Crossrefs

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

Cf. A293306.

Sequence in context: A106236 A270640 A139136 * A348218 A138002 A261877

Adjacent sequences: A122789 A122790 A122791 * A122793 A122794 A122795

Keyword

nonn

Author

Michael Somos, Sep 11 2006

Status

approved