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A053279
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A '7th-order' mock theta function.
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6
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1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 3, 2, 3, 2, 3, 3, 4, 3, 4, 4, 5, 5, 6, 5, 7, 6, 8, 7, 9, 8, 10, 10, 11, 11, 13, 12, 15, 14, 17, 16, 19, 18, 21, 21, 23, 23, 27, 26, 30, 29, 33, 33, 37, 36, 41, 41, 46, 46, 51, 51, 56, 57, 62, 63, 69, 69, 77, 77, 84, 85, 93, 94, 102, 104, 112
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OFFSET
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0,11
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LINKS
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FORMULA
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G.f.: g(q^2, q^7), where g(x, q) = sum for n >= 1 of q^(n(n-1))/((1-x)(1-q/x)(1-q x)(1-q^2/x)...(1-q^(n-1) x)(1-q^n/x)).
a(n) ~ exp(Pi*sqrt(2*n/21)) / (2^(3/2) * sin(2*Pi/7) * sqrt(7*n)). - Vaclav Kotesovec, Jun 14 2019
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MATHEMATICA
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Series[Sum[q^(7n(n-1))/Product[1-q^Abs[7k+2], {k, -n, n-1}], {n, 1, 4}], {q, 0, 100}]
nmax = 100; CoefficientList[Series[Sum[x^(7*k*(k-1))/Product[1-x^Abs[7*j+2], {j, -k, k-1}], {k, 1, Floor[Sqrt[nmax/7]]+1}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Jun 14 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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