Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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