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A053271
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Coefficients of the '6th-order' mock theta function sigma(q).
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9
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0, 1, 1, 2, 3, 3, 5, 7, 8, 11, 14, 17, 22, 28, 33, 41, 51, 60, 74, 89, 105, 127, 151, 177, 210, 248, 289, 340, 398, 461, 537, 624, 719, 832, 960, 1101, 1267, 1453, 1660, 1899, 2167, 2465, 2807, 3190, 3614, 4097, 4638, 5237, 5915, 6671, 7507, 8450, 9498
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OFFSET
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0,4
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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Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, p. 13.
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LINKS
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FORMULA
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G.f.: sigma(q) = Sum_{n >= 0} q^((n+1)(n+2)/2) (1+q)(1+q^2)...(1+q^n)/((1-q)(1-q^3)...(1-q^(2n+1))).
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MATHEMATICA
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Series[Sum[q^((n+1)(n+2)/2) Product[1+q^k, {k, 1, n}]/Product[1-q^k, {k, 1, 2n+1, 2}], {n, 0, 12}], {q, 0, 100}]
nmax = 100; CoefficientList[Series[Sum[x^((k+1)*(k+2)/2) * Product[1+x^j, {j, 1, k}]/Product[1-x^j, {j, 1, 2*k+1, 2}], {k, 0, Floor[Sqrt[2*nmax]]}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Jun 12 2019 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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