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%I #46 Sep 08 2022 08:46:08
%S 1,1,4,14,64,316,1728,10267,65536,445375,3200000,24172676,191102976,
%T 1575167569,13492928512,119786923326,1099511627776,10412878353556,
%U 101559956668416,1018460448140640,10485760000000000,110692335104026963,1196683881290399744
%N a(n) = floor(sqrt((2*n)^n)).
%C Floor(sqrt((2*n)^n)) = floor(sqrt((2*n)^n+1)) since the +1 within the square root function is unneeded for n > 0 and also at n=0, since 0^0 = 1 (interpreted algebraically, à la Knuth). - _Greg Huber_, Aug 07 2018
%H G. C. Greubel, <a href="/A242764/b242764.txt">Table of n, a(n) for n = 0..640</a> (terms 0..50 from Vincenzo Librandi)
%H D. E. Knuth, <a href="https://www.jstor.org/stable/2325085">Two Notes on Notation</a>, The American Mathematical Monthly, 99 (1992), 403-422.
%t Join[{1}, Floor[Sqrt[Array[(2 #)^# + 1 &, 30]]]]
%o (Magma) [Floor(Sqrt((2*n)^n+1)): n in [0..30]];
%o (PARI) vector(30, n, n--; floor(sqrt((2*n)^n))) \\ _G. C. Greubel_, Aug 19 2018
%Y Cf. A000312.
%K nonn,easy
%O 0,3
%A _Vincenzo Librandi_, May 27 2014
%E Name edited by _Greg Huber_, Aug 07 2018
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