A233203 a(n) = floor(n^n / 2^n).

1, 0, 1, 3, 16, 97, 729, 6433, 65536, 756680, 9765625, 139312339, 2176782336, 36972058910, 678223072849, 13363461010158, 281474976710656, 6311342330065435, 150094635296999121, 3773536025353076151, 100000000000000000000, 2785962590401641140642, 81402749386839761113321

Offset: 0

Author

Alex Ratushnyak, Dec 05 2013

Keywords

• nonn

Examples

			a(5) = floor(5^5 / 2^5) = floor(3125 / 32) = 97.
		

Crossrefs

Cf. A000079, A000312, A178537 (n^n mod 2^n for odd n), A206344.

Bisection gives: A062206 (even part).

Programs

Maple

A233203:=n->floor((n/2)^n); seq(A233203(n), n=0..30); # Wesley Ivan Hurt, Feb 26 2014

Mathematica

Table[Floor[(n/2)^n], {n, 0, 30}] (* Wesley Ivan Hurt, Feb 26 2014 *)

PARI

a(n) = n^n\2^n; \\ Michel Marcus, Dec 17 2024

Python

for n in range(33): print(n**n >> n, end=', ')

Formula

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