A168658 a(n) = ceiling(n^n/2).

1, 1, 2, 14, 128, 1563, 23328, 411772, 8388608, 193710245, 5000000000, 142655835306, 4458050224128, 151437553296127, 5556003412779008, 218946945190429688, 9223372036854775808, 413620130943168382089

Offset: 0

Author

Zerinvary Lajos, Dec 02 2009

Keywords

• nonn
• easy

Comments

Number of functions of [n] to [n] (endofunctions of degree n) up to complement to n+1.

There is only one function, and only when n=2k-1 is odd, fixed by n+1-complement, the constant function with value k.

Examples

			Ceiling(6^6/2) = 23328.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..300

Crossrefs

Cf. A000312 (all endofunctions of degree n)

Cf. A057065 (floor of n^n / 2).

Programs

Magma

[Ceiling(n^n/2): n in [0..20]]; // Vincenzo Librandi, Aug 29 2011

Mathematica

Join[{1}, Table[Ceiling[n^n/2], {n, 1, 25}]] (* G. C. Greubel, Jul 28 2016 *)

PARI

a(n) = ceil(n^n/2); \\ Michel Marcus, Feb 18 2016

Sage

[ceil(n^n/2) for n in range(0,21)]#

Formula

a(n) = ceiling(A000312(n)/2).