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Search: id:A053275
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| A053275 |
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Coefficients of the '7th order' mock theta function F_0(q) |
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+0
13
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| 1, 1, 0, 1, 1, 1, 0, 2, 1, 2, 1, 2, 1, 3, 2, 3, 3, 3, 2, 5, 3, 5, 4, 6, 5, 7, 5, 7, 7, 9, 7, 11, 9, 11, 11, 13, 12, 15, 13, 17, 16, 19, 17, 23, 21, 24, 23, 27, 26, 32, 29, 34, 34, 38, 37, 44, 42, 48, 48, 54, 52, 60, 58, 66, 67, 73, 72, 82, 81, 90, 90, 100, 99, 111, 110, 121, 123
(list; graph; listen)
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OFFSET
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0,8
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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
Dean Hickerson, On the seventh order mock theta functions, Inventiones Mathematicae, 94 (1988) 661-677
Srinivasa Ramanujan, Collected Papers, Chelsea, New York, 1962, pp. 354-355
Atle Selberg, Uber die Mock-Thetafunktionen siebenter Ordnung, Arch. Math. Naturvidenskab, 41 (1938) 3-15
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FORMULA
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G.f.: F_0(q) = sum for n >= 0 of q^n^2/((1-q^(n+1))(1-q^(n+2))...(1-q^(2n)))
a(n) = number of partitions of 7n with rank == 0 (mod 7) minus number with rank == 2 (mod 7)
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MATHEMATICA
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Series[Sum[q^n^2/Product[1-q^k, {k, n+1, 2n}], {n, 0, 10}], {q, 0, 100}]
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CROSSREFS
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Other '7th order' mock theta functions are at A053276, A053277, A053278, A053279, A053280.
Sequence in context: A085029 A008622 A029414 this_sequence A025816 A025813 A161231
Adjacent sequences: A053272 A053273 A053274 this_sequence A053276 A053277 A053278
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KEYWORD
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nonn,easy
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AUTHOR
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Dean Hickerson (dean.hickerson(AT)yahoo.com), Dec 19 1999
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