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Search: id:A053259
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| A053259 |
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Coefficients of the '5th order' mock theta function phi_1(q) |
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+0
12
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| 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 2, 1, 0, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 2, 1, 2, 3, 2, 2, 3, 3, 2, 2, 2, 3, 3, 2, 3, 4, 2, 2, 4, 4, 3, 3, 4, 4, 4, 3, 4, 5, 4, 4, 5, 5, 4, 4, 5, 6, 5, 4, 6, 7, 5, 5, 6, 7, 6, 6, 7, 7, 7, 6, 8, 9, 7, 7, 9
(list; graph; listen)
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OFFSET
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0,26
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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Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, pp. 19, 22, 25
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.: phi_1(q) = sum for n >= 0 of q^(n+1)^2 (1+q)(1+q^3)...(1+q^(2n-1))
a(n) = number of partitions of n into odd parts such that each occurs at most twice, the largest part is unique and if k occurs as a part then all smaller positive odd numbers occur
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MATHEMATICA
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Series[Sum[q^(n+1)^2 Product[1+q^(2k-1), {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, A053257, A053258, A053260, A053261, A053262, A053263, A053264, A053265, A053266, A053267.
Sequence in context: A081396 A100544 A130654 this_sequence A092876 A024940 A054635
Adjacent sequences: A053256 A053257 A053258 this_sequence A053260 A053261 A053262
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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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