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Search: id:A006304
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| A006304 |
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Taylor series from Ramanujan's Lost Notebook.
(Formerly M0685)
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+0
3
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| 0, 1, 2, 3, 5, 8, 11, 16, 23, 31, 43, 58, 76, 101, 132, 170, 219, 280, 354, 447, 562, 699, 869, 1076, 1323, 1625, 1987, 2418, 2937, 3556, 4289, 5162, 6196, 7413, 8853, 10547, 12530, 14860, 17586, 20763, 24474, 28792, 33802, 39624, 46368, 54163
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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The "second order" mock theta function A(q). [From Jeremy Lovejoy (lovejoy(AT)liafa.jussieu.fr), Dec 19 2008]
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REFERENCES
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G. E. Andrews, Mordell integrals and Ramanujan's "Lost" Notebook, pp. 10-48 of Analytic Number Theory (Philadelphia 1980), Lect. Notes Math. 899 (1981).
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]
Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, p. 8.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..1000
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FORMULA
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G.f.: sum for n >= 0 of q^(n+1) (1+q^2)(1+q^4)...(1+q^(2n))/((1-q)(1-q^3)...(1-q^(2n+1)))
G.f.: sum for n >= 0 of q^(n+1)^2 (1+q)(1+q^3)...(1+q^(2n-1))/((1-q)(1-q^3)...(1-q^(2n+1)))^2
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MATHEMATICA
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Series[Sum[q^(n+1)^2 Product[1+q^(2k-1), {k, 1, n}]/Product[1-q^(2k-1), {k, 1, n+1}]^2, {n, 0, 9}], {q, 0, 100}]
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CROSSREFS
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Cf. A006305, A006306.
Sequence in context: A101018 A006336 A070228 this_sequence A039847 A046938 A060677
Adjacent sequences: A006301 A006302 A006303 this_sequence A006305 A006306 A006307
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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Corrected and extended by Dean Hickerson (dean.hickerson(AT)yahoo.com), Dec 13 1999
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