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 A053267 Coefficients of the '5th order' mock theta function Psi(q). 14
 0, 0, 1, 0, 1, 1, 1, 1, 2, 1, 2, 2, 3, 2, 4, 3, 4, 4, 5, 5, 7, 6, 8, 8, 9, 9, 12, 11, 14, 14, 16, 16, 20, 19, 23, 24, 27, 27, 32, 32, 37, 38, 43, 44, 51, 51, 58, 61, 67, 69, 78, 80, 89, 93, 102, 106, 118, 121, 134, 140, 153, 159, 175, 181, 198, 207, 224, 234, 256, 265, 288 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,9 REFERENCES George E. Andrews and Frank G. Garvan, Ramanujan's "lost" notebook VI: The mock theta conjectures, Advances in Mathematics, 73 (1989) 242-255 Dean Hickerson, A proof of the mock theta conjectures, Inventiones Mathematicae, 94 (1988) 639-660 Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, pp. 18, 20 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..10000 (terms 0..1000 from G. C. Greubel) FORMULA G.f.: Psi(q) = -1 + sum for n >= 0 of q^(5n^2)/((1-q^2)(1-q^3)(1-q^7)(1-q^8)...(1-q^(5n+2))). a(n) ~ exp(Pi*sqrt(2*n/15)) / (5^(3/4)*sqrt(2*phi*n)), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio. - Vaclav Kotesovec, Jun 12 2019 MATHEMATICA Series[Sum[q^(5n^2)/Product[1-q^Abs[5k+2], {k, -n, n}], {n, 0, 4}], {q, 0, 100}]-1 nmax = 100; CoefficientList[Series[-1 + Sum[x^(5*k^2)/ Product[1-x^Abs[5*j+2], {j, -k, k}], {k, 0, Floor[Sqrt[nmax/5]]}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Jun 12 2019 *) CROSSREFS Other '5th order' mock theta functions are at A053256, A053257, A053258, A053259, A053260, A053261, A053262, A053263, A053264, A053265, A053266. Sequence in context: A051275 A025799 A282537 * A058768 A127682 A127685 Adjacent sequences:  A053264 A053265 A053266 * A053268 A053269 A053270 KEYWORD nonn,easy AUTHOR Dean Hickerson, Dec 19 1999 STATUS approved

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Last modified May 29 20:42 EDT 2020. Contains 334710 sequences. (Running on oeis4.)