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Search: id:A002122
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| A002122 |
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a(n) = Sum_{t=0..n} g(t)*g(n-t) where g(t) = A002121(t).
(Formerly M0273 N0096)
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+0
1
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| 1, 0, -2, 2, 3, -4, -1, 8, -1, -10, 9, 16, -18, -12, 42, 4, -58, 40, 82, -88, -54, 188, 18, -248, 151, 354, -338, -260, 760, 120, -1031, 574, 1460, -1324, -1076, 2948, 542, -3962, 2075, 5644, -4868, -4290, 11035, 2418, -14900, 7346, 21300, -17652, -16323, 40442, 9768, -54476, 25675, 78290, -62456
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Arises in studying the Goldbach conjecture.
The last negative term appears to be a(485). - T. D. Noe, Dec 05 2006
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REFERENCES
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P. A. MacMahon, Properties of prime numbers deduced from the calculus of symmetric functions, Proc. London Math. Soc., 23 (1923), 290-316. [Coll. Papers, Vol. II, pp. 354-382] [The sequence G_n]
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
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.: 1/(1+Sum_{k>0} (-x)^prime(k))^2.
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CROSSREFS
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Cf. A002121.
Sequence in context: A087824 A008951 A119473 this_sequence A105689 A117632 A127731
Adjacent sequences: A002119 A002120 A002121 this_sequence A002123 A002124 A002125
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KEYWORD
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sign
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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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Edited by Vladeta Jovovic (vladeta(AT)eunet.rs), Mar 29 2003
Entry revised by N. J. A. Sloane (njas(AT)research.att.com), Dec 04 2006
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