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Search: id:A053257
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| A053257 |
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Coefficients of the '5th order' mock theta function f_1(q) |
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+0
12
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| 1, 0, 1, -1, 1, -1, 2, -2, 1, -1, 2, -2, 2, -2, 2, -3, 3, -2, 3, -4, 4, -4, 4, -5, 5, -4, 5, -6, 6, -6, 7, -8, 7, -7, 8, -9, 10, -9, 10, -12, 11, -11, 13, -14, 14, -15, 16, -17, 17, -16, 19, -21, 20, -21, 23, -25, 25, -25, 27, -29, 30, -30, 32, -35, 35, -35, 39, -41, 41, -43, 45, -49, 50, -49, 53, -57, 58, -59, 63, -67, 68
(list; graph; listen)
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OFFSET
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0,7
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REFERENCES
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George E. Andrews, The fifth and seventh order mock theta functions, Trans. Amer. Math. Soc., 293 (1986) 113-134
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, Collected Papers, Chelsea, New York, 1962, pp. 354-355
Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, pp. 19, 22
George N. Watson, The mock theta functions (2), Proc. London Math. Soc., series 2, 42 (1937) 274-304
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FORMULA
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G.f.: f_1(q) = sum for n >= 0 of q^(n^2+n)/((1+q)(1+q^2)...(1+q^n))
Consider partitions of n into parts differing by at least 2 and with smallest part at least 2. a(n) = number of them with largest part even minus number with largest part odd
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MATHEMATICA
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Series[Sum[q^(n^2+n)/Product[1+q^k, {k, 1, n}], {n, 0, 9}], {q, 0, 100}]
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CROSSREFS
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Other '5th order' mock theta functions are at A053256, A053258, A053259, A053260, A053261, A053262, A053263, A053264, A053265, A053266, A053267.
Sequence in context: A087011 A000174 A156268 this_sequence A151702 A151552 A160418
Adjacent sequences: A053254 A053255 A053256 this_sequence A053258 A053259 A053260
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KEYWORD
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sign,easy
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AUTHOR
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Dean Hickerson (dean.hickerson(AT)yahoo.com), Dec 19 1999
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