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A053270
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Coefficients of the '6th-order' mock theta function rho(q).
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11
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1, 2, 3, 4, 6, 8, 11, 14, 18, 24, 30, 38, 47, 58, 72, 88, 108, 130, 156, 188, 225, 268, 318, 376, 444, 522, 612, 716, 834, 972, 1129, 1308, 1512, 1744, 2010, 2310, 2652, 3038, 3474, 3968, 4524, 5152, 5857, 6650, 7542, 8540, 9660, 10912, 12312, 13878
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OFFSET
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0,2
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REFERENCES
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Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, pp. 3, 13
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LINKS
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FORMULA
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G.f.: rho(q) = Sum_{n >= 0} ( q^(n(n+1)/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(n+1)/2) Product[1+q^k, {k, 1, n}]/Product[1-q^k, {k, 1, 2n+1, 2}], {n, 0, 13}], {q, 0, 100}]
nmax = 100; CoefficientList[Series[Sum[x^(k*(k+1)/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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