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Search: id:A053260
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| A053260 |
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Coefficients of the '5th order' mock theta function psi_0(q) |
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+0
12
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| 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 1, 2, 2, 2, 3, 3, 2, 3, 3, 3, 3, 4, 4, 4, 5, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 9, 8, 9, 10, 9, 11, 11, 11, 12, 13, 13, 14, 15, 15, 16, 17, 17, 18, 19, 19, 21, 22, 22, 24, 25, 25, 27, 28, 29, 30, 32, 32, 34, 36, 36, 39, 40, 41, 44, 45, 46
(list; graph; listen)
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OFFSET
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0,14
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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
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Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, pp. 19, 21, 22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.: psi_0(q) = sum for n >= 0 of q^((n+1)(n+2)/2) (1+q)(1+q^2)...(1+q^n)
a(n) = number of partitions of n such that each part occurs at most twice, the largest part is unique, and if k occurs as a part then all smaller positive integers occur
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MATHEMATICA
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Series[Sum[q^((n+1)(n+2)/2) Product[1+q^k, {k, 1, n}], {n, 0, 12}], {q, 0, 100}]
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CROSSREFS
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Other '5th order' mock theta functions are at A053256, A053257, A053258, A053259, A053261, A053262, A053263, A053264, A053265, A053266, A053267.
Sequence in context: A102382 A024890 A007895 this_sequence A140223 A014643 A118382
Adjacent sequences: A053257 A053258 A053259 this_sequence A053261 A053262 A053263
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KEYWORD
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nonn,easy
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AUTHOR
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Dean Hickerson (dean(AT)math.ucdavis.edu), Dec 19 1999
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