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a(n) = floor(n^(n + 1/2)).
2

%I #13 Dec 10 2016 08:52:27

%S 0,1,5,46,512,6987,114283,2178889,47453132,1162261467,31622776601,

%T 946271759726,30886277963534,1092031726879989,41577322420731606,

%U 1695955744851044543,73786976294838206464,3410798977520981898013

%N a(n) = floor(n^(n + 1/2)).

%C By Stirling's approximation, a(n) ~ n! e^n /sqrt(2 pi).

%H Harvey P. Dale, <a href="/A127304/b127304.txt">Table of n, a(n) for n = 0..386</a>

%p Digits := 80 : A127304 := proc(n) floor(n^(n+1/2)) ; end: seq(A127304(n),n=0..30) ; # _R. J. Mathar_, Nov 01 2007

%t Table[Floor[n^(n+1/2)],{n,0,20}] (* _Harvey P. Dale_, Dec 10 2016 *)

%Y Cf. A000312, A127265.

%K nonn

%O 0,3

%A _Leroy Quet_, Mar 28 2007

%E More terms from _R. J. Mathar_, Nov 01 2007