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Search: id:A053254
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| A053254 |
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Coefficients of the '3rd order' mock theta function nu(q) |
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+0
9
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| 1, -1, 2, -2, 2, -3, 4, -4, 5, -6, 6, -8, 10, -10, 12, -14, 15, -18, 20, -22, 26, -29, 32, -36, 40, -44, 50, -56, 60, -68, 76, -82, 92, -101, 110, -122, 134, -146, 160, -176, 191, -210, 230, -248, 272, -296, 320, -350, 380, -410, 446, -484, 522, -566, 612, -660, 715, -772, 830, -896, 966, -1038
(list; graph; listen)
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OFFSET
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0,3
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REFERENCES
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Leila A. Dragonette, Some asymptotic formulae for the mock theta functions of Ramanujan, Trans. Amer. Math. Soc., 72 (1952) 474-500
Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, p. 31
George N. Watson, The final problem: an account of the mock theta functions, J. London Math. Soc., 11 (1936) 55-80
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FORMULA
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G.f.: nu(q) = sum for n >= 0 of q^(n(n+1))/((1+q)(1+q^3)...(1+q^(2n+1)))
(-1)^n a(n) = number of partitions of n in which even parts are distinct and if k occurs then so does every positive even number less than k
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MATHEMATICA
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Series[Sum[q^(n(n+1))/Product[1+q^(2k+1), {k, 0, n}], {n, 0, 9}], {q, 0, 100}]
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CROSSREFS
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Other '3rd order' mock theta functions are at A000025, A053250, A053251, A053252, A053253, A053255.
Sequence in context: A000929 A029146 A029053 this_sequence A067357 A051059 A132967
Adjacent sequences: A053251 A053252 A053253 this_sequence A053255 A053256 A053257
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KEYWORD
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sign,easy
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AUTHOR
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Dean Hickerson (dean(AT)math.ucdavis.edu), Dec 19 1999
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