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a(n) = floor(n^n/2).
5

%I #19 Sep 08 2022 08:45:01

%S 0,0,2,13,128,1562,23328,411771,8388608,193710244,5000000000,

%T 142655835305,4458050224128,151437553296126,5556003412779008,

%U 218946945190429687,9223372036854775808,413620130943168382088,19673204037648268787712,989209827830156794561989

%N a(n) = floor(n^n/2).

%H Harvey P. Dale, <a href="/A057065/b057065.txt">Table of n, a(n) for n = 0..300</a>

%F a(n) = floor( A000312(n)/2 ).

%e a(5) = floor(5^5/2) = floor(3125/2) = 1562.

%t Join[{0}, Table[Floor[n^n/2], {n, 20}]] (* _Harvey P. Dale_, May 19 2012 *)

%o (Sage) [floor(n^n/2) for n in range(0,17)] # _Zerinvary Lajos_, Dec 02 2009

%o (PARI) a(n) = n^n\2; \\ _Michel Marcus_, Feb 18 2016

%o (Magma) [Floor(n^n/2): n in [0..20]]; // _Vincenzo Librandi_, Feb 18 2016

%Y Cf. A000312.

%K nonn

%O 0,3

%A _Henry Bottomley_, Jul 31 2000

%E More terms from _Harvey P. Dale_, May 19 2012