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%I #11 May 20 2016 13:35:31
%S 2,2,14,150,2362,49210,1280582,40045166,1464047858,61310662578,
%T 2894855376382,152184891889030,8817255144288554,558260148630165098,
%U 38351949989325264182,2841496569324942436830
%N a(n) = ((2*n+1)^(n+1) + (-1)^n)/(n+1)^2.
%C When searching for the smallest k such that n^k + 1 is not squarefree, I noticed that if n is even then n^(n+1) + 1 is not squarefree, and if n is of the form 4*j + 1 (j>0) then n^((n+1)/2) + 1 is not squarefree.
%F a(n) = Sum_{k = 0..n} (-1)^(n - k)*2^(k+1)*(n+1)^(k-1)*C(n+1, n - k).
%t Table[((2n + 1)^(n + 1) + (-1)^n)/(n + 1)^2, {n, 0, 15}] (* _Alonso del Arte_, May 19 2016 *)
%Y Cf. A081215.
%K nonn,easy
%O 0,1
%A _Gionata Neri_, May 19 2016
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