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A106508
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Expansion of psi(x)^4 * chi(-x^2)^2 in powers of x where psi(), chi() are Ramanujan theta functions.
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3
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1, 4, 4, 0, 2, 0, -8, 0, -5, -16, 4, 0, -10, 0, -8, 0, 9, 8, 0, 0, 14, 0, 16, 0, -10, 32, 4, 0, 0, 0, 8, 0, 14, -20, -20, 0, 2, 0, 0, 0, -11, -16, -20, 0, -32, 0, 16, 0, 0, -40, 4, 0, 14, 0, -8, 0, -9, 32, -20, 0, 26, 0, 0, 0, 2, 36, 28, 0, 0, 0, 16, 0, 16, 0, 28, 0, -22, 0, 0, 0, 14, 56, -16, 0, 0, 0, -40, 0, 0
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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Expansion of q^(-1/3) * eta(q^2)^10 / (eta(q)^4 * eta(q^4)^2) in powers of q.
Euler transform of period 4 sequence [4, -6, 4, -4, ...].
a(n) = (-1)^n * A187149(n). a(4*n + 3) = a(8*n + 5) = 0.
G.f. Product_{k>0} (1 + x^k)^4 (1 - x^(2*k))^4 / (1 + x^(2*k))^2.
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EXAMPLE
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1 + 4*x + 4*x^2 + 2*x^4 - 8*x^6 - 5*x^8 - 16*x^9 + 4*x^10 - 10*x^12 + ...
q + 4*q^4 + 4*q^7 + 2*q^13 - 8*q^19 - 5*q^25 - 16*q^28 + 4*q^31 - 10*q^37 + ...
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MATHEMATICA
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a[n_]:= SeriesCoefficient[(x^(-1/2)/16)*EllipticTheta[2, 0, x^(1/2)]^4* QPochhammer[x^2, x^4]^2, {x, 0, n}]; Table[a[n], {n, 0, 50}] (* G. C. Greubel, Jan 04 2018 *)
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PROG
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(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^10 / (eta(x^4 + A)^2 * eta(x + A)^4), 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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