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A316662
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Expansion of f(x, x^2) * psi(x^3)^3 in powers of x where psi() is a Ramanujan theta function and f(, ) is Ramanujan's general theta function.
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1
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1, 1, 1, 3, 3, 4, 3, 4, 6, 4, 7, 7, 7, 9, 10, 7, 7, 9, 12, 12, 9, 16, 13, 15, 13, 12, 13, 16, 19, 13, 18, 16, 19, 21, 19, 20, 21, 21, 24, 19, 22, 24, 22, 27, 25, 21, 21, 27, 30, 32, 27, 28, 30, 37, 25, 31, 34, 28, 36, 28, 31, 28, 31, 48, 36, 36, 38, 31, 42, 37
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OFFSET
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0,4
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COMMENTS
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LINKS
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FORMULA
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Expansion of q^(-7/6) * eta(q^2) * eta(q^6)^5 / (eta(q) * eta(q^3)) in powers of q.
Expansion of b(x^2) * c(x^2)^2 / sqrt(b(x) * c(x)/3) in powers of x where b(), c() are cubic AGM theta functions.
Expansion of psi(x^3) * f(-x^6)^3 / chi(-x) = f(-x^6)^4 / (chi(-x) * chi(-x^3)) = f(-x^6)^5 /(f(-x^3) * chi(-x)) in powers of x where psi(), chi(), f() are Ramanujan theta functions.
G.f.: Product_{k>0} (1 + x^k) * (1 + x^(3*k)) * (1 - x^(6*k))^4.
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EXAMPLE
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G.f. = 1 + x + x^2 + 3*x^3 + 3*x^4 + 4*x^5 + 3*x^6 + 4*x^7 + 6*x^8 + ...
G.f. = q^7 + q^13 + q^19 + 3*q^25 + 3*q^31 + 4*q^37 + 3*q^43 + 4*q^49 + ...
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MATHEMATICA
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a[ n_] := SeriesCoefficient[ QPochhammer[ x^6]^4 / (QPochhammer[ x, x^2] QPochhammer[ x^3, x^6]), {x, 0, n}];
a[ n_] := SeriesCoefficient[ QPochhammer[ x^6]^5 / (QPochhammer[ x, x^2] QPochhammer[ x^3]), {x, 0, n}];
a[ n_] := SeriesCoefficient[ QPochhammer[ x^2] QPochhammer[ x^6]^5 / (QPochhammer[ x] QPochhammer[x^3]), {x, 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) * eta(x^6 + A)^5 / (eta(x + A) * eta(x^3 + A)), n))};
(Magma) Basis( ModularForms( Gamma0(36), 2), 427) [8];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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