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Search: id:A006306
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| A006306 |
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Taylor series from Ramanujan's Lost Notebook.
(Formerly M0163)
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+0
3
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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; listen)
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OFFSET
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0,4
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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).
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FORMULA
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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
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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
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Cf. A006304, A006305.
Sequence in context: A102627 A088296 A093890 this_sequence A083711 A018783 A114326
Adjacent sequences: A006303 A006304 A006305 this_sequence A006307 A006308 A006309
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KEYWORD
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sign,easy,nice
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AUTHOR
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njas
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EXTENSIONS
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Corrected and extended by Dean Hickerson (dean(AT)math.ucdavis.edu), Dec 13 1999
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