%I #19 Sep 08 2022 08:45:49
%S 1,1,2,14,128,1563,23328,411772,8388608,193710245,5000000000,
%T 142655835306,4458050224128,151437553296127,5556003412779008,
%U 218946945190429688,9223372036854775808,413620130943168382089
%N a(n) = ceiling(n^n/2).
%C Number of functions of [n] to [n] (endofunctions of degree n) up to complement to n+1.
%C There is only one function, and only when n=2k-1 is odd, fixed by n+1-complement, the constant function with value k.
%H Vincenzo Librandi, <a href="/A168658/b168658.txt">Table of n, a(n) for n = 0..300</a>
%F a(n) = ceiling(A000312(n)/2).
%e Ceiling(6^6/2) = 23328.
%t Join[{1}, Table[Ceiling[n^n/2], {n, 1, 25}]] (* _G. C. Greubel_, Jul 28 2016 *)
%o (Sage) [ceil(n^n/2) for n in range(0,21)]#
%o (Magma)[Ceiling(n^n/2): n in [0..20]]; // _Vincenzo Librandi_, Aug 29 2011
%o (PARI) a(n) = ceil(n^n/2); \\ _Michel Marcus_, Feb 18 2016
%Y Cf. A000312 (all endofunctions of degree n)
%Y Cf. A057065 (floor of n^n / 2).
%K nonn,easy
%O 0,3
%A _Zerinvary Lajos_, Dec 02 2009