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%I #11 May 08 2013 05:06:13
%S 4,27,64,115,182,263,359,470,596,736,891,1061,1246,1445,1660,1889,
%T 2132,2391,2664,2953,3256,3573,3906,4253,4615,4992,5384,5790,6211,
%U 6647,7098,7563,8044,8539,9049,9573,10113,10667,11236,11820,12418,13031,13659
%N a(n) = floor((n+2)^(n+2)/n^n).
%F a(n) - e^2(n+1)^2 is bounded. Conjecture: there's a constant c = 2.462... such that a(n) = floor(e^2*(n+1)^2-c).
%F I believe (n+2)^(n+2)/n^n = e^2(n^2 + 2n + 2/3 + o(1)), so the conjecture should be correct (with perhaps finitely many exceptions) with c = e^2/3 = 2.463.... - _Charles R Greathouse IV_, May 07 2013
%o (PARI) a(n)=(1+2./n)^n*(n+2)^2\1 \\ _Charles R Greathouse IV_, May 07 2013
%Y Cf. A060644.
%K nonn
%O 0,1
%A _Benoit Cloitre_, Dec 03 2002
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