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%I #10 Mar 26 2018 16:09:19
%S 4,8,52,492,64132,800048,137270956,1860277044,357975249028,
%T 1036802293087624,15013817846943908,47192717955016924592,
%U 10360599532897359064120,154361699651715243559788,34589385964790856394651396,118349529407778329236413352408,412825418773807104132857739017404
%N (1/p)*(binomial(2*p,p)+2*(p-1)), where p = n-th prime.
%C For p odd, this is the number of p-element subsets of {1, 2, ..., 2p} whose sum is divisible by p.
%D R. Honsberger, Mathematical Chestnuts from Around the World, MAA, 2001; see p. 220-223.
%H StackExchange, <a href="https://mathematica.stackexchange.com/questions/169735/easy-number-theory-problem">Easy number theory problem</a>, Mar 25 2018
%t (1/# (Binomial[2#,#]+2(#-1)))&/@Prime[Range[30]] (* _Harvey P. Dale_, Oct 22 2011 *)
%K nonn
%O 1,1
%A _N. J. A. Sloane_, Jul 23 2008