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A261321
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Expansion of (phi(q) / phi(q^3))^2 in powers of q where phi() is a Ramanujan theta function.
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1
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1, 4, 4, -4, -12, -8, 12, 32, 20, -28, -72, -48, 60, 152, 96, -120, -300, -184, 228, 560, 344, -416, -1008, -608, 732, 1756, 1048, -1252, -2976, -1768, 2088, 4928, 2900, -3408, -7992, -4672, 5460, 12728, 7408, -8600, -19944, -11544, 13344, 30800, 17744, -20424
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OFFSET
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0,2
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COMMENTS
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The generating function is associated with a modular equation of degree 3 and is the multiplier denoted by "m". - Michael Somos, Nov 01 2017
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REFERENCES
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B. C. Berndt, Ramanujan's Notebooks Part III, Springer-Verlag, see p. 230 Entry 5(iii), g.f. denoted by multiplier m.
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LINKS
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FORMULA
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Expansion of eta(q^2)^10 * eta(q^3)^4 * eta(q^12)^4 / (eta(q)^4 * eta(q^4)^4 * eta(q^6)^10) in powers of q.
G.f.: (Sum_{k in Z} x^k^2) / (Sum_{k in Z} x^(3*k^2))^2.
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EXAMPLE
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G.f. = 1 + 4*x + 4*x^2 - 4*x^3 - 12*x^4 - 8*x^5 + 12*x^6 + 32*x^7 + ...
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MATHEMATICA
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a[ n_] := SeriesCoefficient[ (EllipticTheta[ 3, 0, q] / EllipticTheta[ 3, 0, q^3])^2, {q, 0, n}];
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PROG
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(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^10 * eta(x^3 + A)^4 * eta(x^12 + A)^4 / (eta(x + A)^4 * eta(x^4 + A)^4 * eta(x^6 + A)^10), 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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