A002122 a(n) = Sum_{t=0..n} g(t)*g(n-t) where g(t) = A002121(t).
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
Offset: 0
Keywords
References
- 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
- P. A. MacMahon, Properties of prime numbers deduced from the calculus of symmetric functions, Proc. London Math. Soc., 23 (1923), 290-316. = Coll. Papers, II, pp. 354-380. [The sequence G_n]
- Index entries for sequences related to Goldbach conjecture
Crossrefs
Cf. A002121.
Programs
-
Haskell
a002122 n = a002122_list !! n a002122_list = uncurry conv $ splitAt 1 a002121_list where conv xs (z:zs) = sum (zipWith (*) xs $ reverse xs) : conv (z:xs) zs -- Reinhard Zumkeller, Mar 21 2014
Formula
G.f.: 1/(1+Sum_{k>0} (-x)^prime(k))^2.
Extensions
Edited by Vladeta Jovovic, Mar 29 2003
Entry revised by N. J. A. Sloane, Dec 04 2006
Comments