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A122792 Expansion of eta(q^2)^2/(eta(q)eta(q^3)) in powers of q. 4

%I

%S 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,

%T 0,104,58,0,144,80,0,198,110,0,268,148,0,360,198,0,480,264,0,634,347,

%U 0,832,454,0,1084,592,0,1404,764,0,1808,982,0,2316,1257,0,2952,1598,0

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

%H Seiichi Manyama, <a href="/A122792/b122792.txt">Table of n, a(n) for n = 0..10000</a>

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

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

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

%t 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 *)

%o (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))}

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

%Y Cf. A293306.

%K nonn

%O 0,4

%A _Michael Somos_, Sep 11 2006

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Last modified July 11 15:58 EDT 2020. Contains 335626 sequences. (Running on oeis4.)