A242764 a(n) = floor(sqrt((2*n)^n)).

1, 1, 4, 14, 64, 316, 1728, 10267, 65536, 445375, 3200000, 24172676, 191102976, 1575167569, 13492928512, 119786923326, 1099511627776, 10412878353556, 101559956668416, 1018460448140640, 10485760000000000, 110692335104026963, 1196683881290399744

Offset: 0

Author

Vincenzo Librandi, May 27 2014

Keywords

• nonn
• easy

Comments

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

Links

• G. C. Greubel, Table of n, a(n) for n = 0..640 (terms 0..50 from Vincenzo Librandi)
• D. E. Knuth, Two Notes on Notation, The American Mathematical Monthly, 99 (1992), 403-422.

Crossrefs

Cf. A000312.

Programs

Magma

[Floor(Sqrt((2*n)^n+1)): n in [0..30]];

Mathematica

Join[{1}, Floor[Sqrt[Array[(2 #)^# + 1 &, 30]]]]

PARI

vector(30, n, n--; floor(sqrt((2*n)^n))) \\ G. C. Greubel, Aug 19 2018

Extensions

Name edited by Greg Huber, Aug 07 2018