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A153176
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Coefficients of the eighth-order mock theta function V_0(q).
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8
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1, 2, 4, 4, 6, 8, 8, 12, 16, 18, 24, 28, 32, 40, 48, 56, 66, 80, 92, 108, 128, 144, 168, 196, 224, 258, 296, 336, 384, 440, 496, 564, 640, 720, 816, 920, 1030, 1160, 1304, 1456, 1632, 1824, 2032, 2268, 2528, 2808, 3120, 3468, 3840, 4258, 4716, 5208, 5760, 6360
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OFFSET
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0,2
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LINKS
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FORMULA
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V_0(q) = -1 + 2*Sum_{n >= 0} q^(n^2)(1+q)(1+q^3)...(1+q^(2n-1))/((1-q)(1-q^3)...(1-q^(2n-1))).
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MATHEMATICA
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nmax = 100; CoefficientList[Series[-1 + 2*Sum[x^(k^2) * Product[(1 + x^(2*j - 1))/(1 - x^(2*j - 1)), {j, 1, k}], {k, 0, Floor[Sqrt[nmax]]}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Jun 12 2019 *)
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PROG
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(PARI) lista(nn) = my(q = qq + O(qq^nn)); gf = -1 + 2* sum(n = 0, nn, q^(n^2) * prod(k = 1, n, 1 + q^(2*k-1)) / prod(k = 1, n, 1 - q^(2*k-1))); Vec(gf) \\ Michel Marcus, Jun 18 2013
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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