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A122792 Expansion of eta(q^2)^2/(eta(q)eta(q^3)) in powers of q. 4
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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 * A138002 A261877 A062296

Adjacent sequences:  A122789 A122790 A122791 * A122793 A122794 A122795

KEYWORD

nonn

AUTHOR

Michael Somos, Sep 11 2006

STATUS

approved

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Last modified June 15 22:19 EDT 2019. Contains 324145 sequences. (Running on oeis4.)