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A053273
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Coefficients of the '6th-order' mock theta function 2 mu(q).
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9
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1, 2, -3, 4, -4, 6, -11, 14, -15, 22, -31, 34, -41, 56, -69, 82, -98, 120, -152, 178, -204, 254, -308, 354, -415, 496, -587, 680, -785, 922, -1084, 1248, -1427, 1664, -1935, 2202, -2517, 2906, -3336, 3798, -4315, 4930, -5636, 6380, -7202, 8194, -9305, 10474, -11801, 13342, -15050
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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Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, p. 13
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LINKS
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FORMULA
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G.f.: 2 mu(q) = 1 + Sum_{n >= 0} (-1)^n q^(n+1) (1+q^n) (1-q)(1-q^3)...(1-q^(2n-1))/((1+q)(1+q^2)...(1+q^(n+1))).
a(n) ~ -(-1)^n * exp(Pi*sqrt(n/3)) / (2*sqrt(3*n)). - Vaclav Kotesovec, Jun 15 2019
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MATHEMATICA
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Series[1+Sum[(-1)^n q^(n+1) (1+q^n) Product[1-q^k, {k, 1, 2n-1, 2}]/Product[1+q^k, {k, 1, n+1}], {n, 0, 99}], {q, 0, 100}]
nmax = 100; CoefficientList[Series[1 + Sum[(-1)^k * x^(k+1) * (1+x^k) * Product[1-x^j, {j, 1, 2*k-1, 2}] / Product[1+x^j, {j, 1, k+1}], {k, 0, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Jun 15 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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