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A134414
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Expansion of eta(q)^2 / (eta(q^2) * eta(q^4)^6) in powers of q.
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5
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1, -2, 0, 0, 8, -12, 0, 0, 39, -56, 0, 0, 152, -208, 0, 0, 513, -684, 0, 0, 1560, -2032, 0, 0, 4382, -5616, 0, 0, 11552, -14592, 0, 0, 28899, -36088, 0, 0, 69168, -85500, 0, 0, 159372, -195312, 0, 0, 355224, -431984, 0, 0, 768885, -928720, 0, 0, 1621296, -1946352, 0, 0, 3339201
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OFFSET
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-1,2
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LINKS
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FORMULA
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Euler transform of period 4 sequence [ -2, -1, -2, 5, ...].
a(4*n+1) = a(4*n+2) = 0.
G.f.: x^(-1) * Product_{k>0} (1 - x^k) / ((1 + x^k) * (1 - x^(4*k))^6).
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EXAMPLE
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1/q - 2 + 8*q^3 - 12*q^4 + 39*q^7 - 56*q^8 + 152*q^11 - 208*q^12 + ...
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MATHEMATICA
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QP = QPochhammer; s = QP[q]^2/(QP[q^2]*QP[q^4]^6) + O[q]^60; CoefficientList[s, q] (* Jean-François Alcover, Nov 27 2015 *)
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PROG
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(PARI) {a(n) = local(A); if( n<-1, 0, n++; A = x * O(x^n); polcoeff( eta(x + A)^2 / (eta(x^2 + A) * eta(x^4 + A)^6), n))}
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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