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

%I M0273 N0096

%S 1,0,-2,2,3,-4,-1,8,-1,-10,9,16,-18,-12,42,4,-58,40,82,-88,-54,188,18,

%T -248,151,354,-338,-260,760,120,-1031,574,1460,-1324,-1076,2948,542,

%U -3962,2075,5644,-4868,-4290,11035,2418,-14900,7346,21300,-17652,-16323,40442,9768,-54476,25675,78290,-62456

%N a(n) = Sum_{t=0..n} g(t)*g(n-t) where g(t) = A002121(t).

%C Arises in studying the Goldbach conjecture.

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

%D 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]

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H T. D. Noe, <a href="/A002122/b002122.txt">Table of n, a(n) for n = 0..1000</a>

%H P. A. MacMahon, <a href="http://plms.oxfordjournals.org/content/s2-23/1/290.extract">Properties of prime numbers deduced from the calculus of symmetric functions</a>, Proc. London Math. Soc., 23 (1923), 290-316. = Coll. Papers, II, pp. 354-380.

%H <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>

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

%o (Haskell)

%o a002122 n = a002122_list !! n

%o a002122_list = uncurry conv $ splitAt 1 a002121_list where

%o conv xs (z:zs) = sum (zipWith (*) xs $ reverse xs) : conv (z:xs) zs

%o -- _Reinhard Zumkeller_, Mar 21 2014

%Y Cf. A002121.

%K sign

%O 0,3

%A _N. J. A. Sloane_.

%E Edited by _Vladeta Jovovic_, Mar 29 2003

%E Entry revised by _N. J. A. Sloane_, Dec 04 2006

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Last modified September 19 12:57 EDT 2019. Contains 327198 sequences. (Running on oeis4.)