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A248395
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q-Expansion of the modular form of weight 3/2, g*theta(4) in Tunnell's notation (see Comments).
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14
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0, 1, 0, 0, 0, 2, 0, 0, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, -4, 0, 0, 0, 2, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, -2, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0
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OFFSET
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0,6
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COMMENTS
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g = Product_{m>=1} ((1-q^(8*m))*(1-q^(16*m)),
theta(t) = Sum_{n=-oo..oo} (q^(t*n^2)).
Although the OEIS does not normally include sequences in which only every fourth term is nonzero, this one is important enough to warrant an exception.
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LINKS
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FORMULA
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Expansion of eta(q^8)*eta(q^16)*theta_{3}(0, q^4)/q in powers of q.
Expansion of eta(q^8)^6/(q*eta(q^4)^2*eta(q^16)). (End)
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MAPLE
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# This produces a list of the first 100 terms:
g:=q*mul((1-q^(8*m))*(1-q^(16*m)), m=1..30);
g:=series(g, q, 100);
th:=t->series( add(q^(t*n^2), n=-50..50), q, 100);
series(g*th(4), q, 100);
seriestolist(%);
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MATHEMATICA
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QP := QPochhammer; a:= CoefficientList[Series[QP[q^8]*QP[q^16]* EllipticTheta[3, 0, q^4], {q, 0, 60}], q]; Join[{0}, Table[a[[n]], {n, 1, 50}]] (* G. C. Greubel, Jul 02 2018 *)
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PROG
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(PARI) q='q+O('q^50); A = eta(q^8)^6/(q*eta(q^4)^2*eta(q^16)); concat([0], Vec(A)) \\ G. C. Greubel, Jul 02 2018
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CROSSREFS
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The nonzero quadrisection is A080966, which has further information and references.
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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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