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A053283
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Coefficients of the '10th-order' mock theta function X(q).
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7
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1, -1, 1, 0, 1, -2, 1, -1, 1, -2, 3, -1, 2, -4, 3, -2, 3, -5, 4, -4, 5, -6, 7, -5, 6, -9, 9, -7, 9, -12, 11, -11, 12, -15, 16, -14, 16, -21, 20, -18, 22, -25, 26, -25, 28, -33, 34, -33, 35, -42, 43, -41, 47, -53, 53, -54, 57, -65, 69, -67, 73, -83, 85, -83, 92, -102, 104, -106, 114, -125, 130, -130, 139, -154
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OFFSET
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0,6
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REFERENCES
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Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, p. 9
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LINKS
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FORMULA
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G.f.: X(q) = Sum_{n >= 0} (-1)^n q^n^2/((1+q)(1+q^2)...(1+q^(2n))).
a(n) ~ (-1)^n * exp(Pi*sqrt(n/10)) / (2*5^(1/4)*sqrt(phi*n)), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio. - Vaclav Kotesovec, Jun 12 2019
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MATHEMATICA
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Series[Sum[(-1)^n q^n^2/Product[1+q^k, {k, 1, 2n}], {n, 0, 10}], {q, 0, 100}]
nmax = 100; CoefficientList[Series[Sum[(-1)^k * x^(k^2) / Product[1+x^j, {j, 1, 2*k}], {k, 0, Floor[Sqrt[nmax]]}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Jun 11 2019 *)
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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STATUS
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approved
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