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A006306
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Taylor series from Ramanujan's Lost Notebook.
(Formerly M0163)
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2
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1, -1, 1, 2, -1, -4, 1, 5, -2, -5, 4, 7, -4, -11, 3, 13, -6, -14, 9, 18, -7, -24, 8, 29, -14, -32, 17, 38, -18, -50, 20, 58, -25, -63, 33, 77, -35, -94, 36, 108, -48, -122, 60, 141, -63, -170, 70, 195, -87, -215, 101, 250, -110, -294, 124, 333, -146, -371, 173, 424, -190, -492, 206, 554, -245, -617, 283
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Contribution from Jeremy Lovejoy (lovejoy(AT)liafa.jussieu.fr), Dec 19 2008: (Start)
Coefficients of the "second order" mock theta function mu(q).
|a(n)| is the number of partitions of n without repeated odd parts whose M2-rank is even minus the number of partitions of n without repeated odd parts whose M2-rank is odd. (End)
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REFERENCES
| G. E. Andrews, Mordell integrals and Ramanujan's "Lost" Notebook, pp. 10-48 of Analytic Number Theory (Philadelphia 1980), Lect. Notes Math. 899 (1981).
K. Bringmann, K. Ono and R. Rhoades, Eulerian series as modular forms, J. Amer. Math. Soc. 21 (2008), 1085-1104. [From Jeremy Lovejoy (lovejoy(AT)liafa.jussieu.fr), Dec 19 2008]
R. J. McIntosh, Second order mock theta functions, Canad. Math. Bull. 50 (2007), 284-290. [From Jeremy Lovejoy (lovejoy(AT)liafa.jussieu.fr), Dec 19 2008]
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| J. Lovejoy and R. Osburn, M_2-rank differences for partitions without repeated odd parts [From Jeremy Lovejoy (lovejoy(AT)liafa.jussieu.fr), Dec 19 2008]
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FORMULA
| G.f.: sum for n >= 0 of (-1)^n q^n^2 (1-q)(1-q^3)...(1-q^(2n-1))/((1+q^2)^2 (1+q^4)^2 ... (1+q^(2n))^2)
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MATHEMATICA
| Series[Sum[(-q)^n^2 Product[(1-q^(2k-1))/(1+q^(2k))^2, {k, 1, n}], {n, 0, 10}], {q, 0, 100}]
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CROSSREFS
| Cf. A006304, A006305.
Sequence in context: A102627 A088296 A093890 * A083711 A018783 A200976
Adjacent sequences: A006303 A006304 A006305 * A006307 A006308 A006309
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KEYWORD
| sign,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Corrected and extended by Dean Hickerson (dean.hickerson(AT)yahoo.com), Dec 13 1999
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