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A002122 a(n) = Sum_{t=0..n} g(t)*g(n-t) where g(t) = A002121(t).
(Formerly M0273 N0096)
+0
1
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)
OFFSET

0,3

COMMENT

Arises in studying the Goldbach conjecture.

The last negative term appears to be a(485). - T. D. Noe, Dec 05 2006

REFERENCES

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).

LINKS

T. D. Noe, Table of n, a(n) for n=0..1000

FORMULA

G.f.: 1/(1+Sum_{k>0} (-x)^prime(k))^2.

CROSSREFS

Cf. A002121.

Sequence in context: A087824 A008951 A119473 this_sequence A105689 A117632 A127731

Adjacent sequences: A002119 A002120 A002121 this_sequence A002123 A002124 A002125

KEYWORD

sign

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com).

EXTENSIONS

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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Last modified November 25 20:09 EST 2009. Contains 167514 sequences.


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