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Search: id:A053262
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| A053262 |
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Coefficients of the 5th order mock theta function chi_0(q) |
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+0
12
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| 1, 1, 1, 2, 1, 3, 2, 3, 3, 5, 3, 6, 5, 7, 7, 9, 7, 12, 11, 13, 13, 17, 15, 21, 20, 24, 24, 29, 28, 36, 35, 40, 42, 50, 48, 58, 58, 67, 70, 80, 79, 93, 95, 106, 111, 125, 127, 145, 149, 166, 172, 191, 196, 222, 229, 250, 262, 289, 298, 330, 343, 373, 391, 427, 442, 486
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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The rank of a partition is its largest part minus the number of parts.
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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Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, pp. 20, 23, 25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.: chi_0(q) = sum for n >= 0 of q^n/((1-q^(n+1))(1-q^(n+2))...(1-q^(2n)))
G.f.: chi_0(q) = 1 + sum for n >= 0 of q^(2n+1)/((1-q^(n+1))(1-q^(n+2))...(1-q^(2n+1)))
a(n) = number of partitions of 5n with rank == 1 (mod 5) minus number with rank == 0 (mod 5)
a(n) = number of partitions of n with unique smallest part and all other parts <= twice the smallest part
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MATHEMATICA
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1+Series[Sum[q^(2n+1)/Product[1-q^k, {k, n+1, 2n+1}], {n, 0, 49}], {q, 0, 100}]
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CROSSREFS
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Other '5th order' mock theta functions are at A053256, A053257, A053258, A053259, A053260, A053261, A053263, A053264, A053265, A053266, A053267.
Sequence in context: A025797 A035386 A029164 this_sequence A007359 A115872 A133926
Adjacent sequences: A053259 A053260 A053261 this_sequence A053263 A053264 A053265
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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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