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 A053268 Coefficients of the '6th-order' mock theta function phi(q). 12
 1, -1, 2, -1, 1, -3, 3, -3, 4, -4, 6, -6, 5, -9, 11, -10, 11, -15, 17, -16, 19, -22, 26, -29, 29, -36, 42, -42, 46, -55, 60, -64, 71, -79, 90, -95, 101, -117, 131, -137, 148, -169, 184, -195, 211, -234, 258, -276, 295, -327, 360, -379, 409, -453, 489, -522, 563, -612, 666, -710, 757, -829, 898 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 REFERENCES Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, pp. 2, 4, 6, 13, 16, 17 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..10000 (corrected and extended previous b-file from G. C. Greubel) George E. Andrews and Dean Hickerson, Ramanujan's "lost" notebook VII: The sixth order mock theta functions, Advances in Mathematics, 89 (1991) 60-105. FORMULA G.f.: phi(q) = sum for n >= 0 of (-1)^n q^n^2 (1-q)(1-q^3)...(1-q^(2n-1))/((1+q)(1+q^2)...(1+q^(2n))). a(n) ~ (-1)^n * exp(Pi*sqrt(n/6)) / (2*sqrt(3*n)). - Vaclav Kotesovec, Jun 15 2019 MATHEMATICA Series[Sum[(-1)^n q^n^2 Product[1-q^k, {k, 1, 2n-1, 2}]/Product[1+q^k, {k, 1, 2n}], {n, 0, 10}], {q, 0, 100}] nmax = 100; CoefficientList[Series[Sum[(-1)^k * x^(k^2) * Product[1-x^j, {j, 1, 2*k-1, 2}] / Product[1+x^j, {j, 1, 2*k}], {k, 0, Floor[Sqrt[nmax]]}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Jun 15 2019 *) CROSSREFS Other '6th-order' mock theta functions are at A053269, A053270, A053271, A053272, A053273, A053274. Sequence in context: A240807 A334347 A283672 * A284828 A101417 A318660 Adjacent sequences:  A053265 A053266 A053267 * A053269 A053270 A053271 KEYWORD sign,easy AUTHOR Dean Hickerson, Dec 19 1999 STATUS approved

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Last modified June 19 21:25 EDT 2021. Contains 345151 sequences. (Running on oeis4.)