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Search: id:A053277
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| A053277 |
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Coefficients of the '7th order' mock theta function F_2(q) |
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+0
6
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| 1, 1, 2, 1, 2, 2, 3, 2, 3, 3, 4, 4, 5, 4, 6, 5, 7, 7, 8, 8, 10, 9, 11, 11, 13, 13, 16, 15, 17, 18, 21, 20, 23, 23, 27, 27, 31, 31, 35, 35, 39, 41, 45, 45, 51, 51, 57, 59, 64, 66, 73, 74, 81, 83, 91, 93, 102, 104, 113, 117, 126, 130, 141, 144, 156, 162, 174, 178, 192, 198, 212
(list; graph; listen)
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OFFSET
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0,3
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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_2(q) = sum for n >= 0 of q^(n(n+1))/((1-q^(n+1))(1-q^(n+2))...(1-q^(2n+1)))
a(n) = number of partitions of 7n+2 with rank == 1 (mod 7) minus number with rank == 2 (mod 7)
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MATHEMATICA
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Series[Sum[q^(n^2+n)/Product[1-q^k, {k, n+1, 2n+1}], {n, 0, 9}], {q, 0, 100}]
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CROSSREFS
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Other '7th order' mock theta functions are at A053275, A053276, A053278, A053279, A053280.
Sequence in context: A008624 A059169 A027349 this_sequence A078661 A029263 A097575
Adjacent sequences: A053274 A053275 A053276 this_sequence A053278 A053279 A053280
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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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