A127642 - OEIS

%I #7 Jan 09 2016 16:37:55

%S -1,0,1,6,19,53,144,384,1010,2652,6960,18271,48007,126292,332679,

%T 877561,2318039,6131032,16236271,43047375,114256746,303570609,

%U 807327311,2148933010,5724699937,15262109996,40717942427,108704057535,290385838171,776171229484

%N Floor(n^n/n!) - ceiling(2^n/n).

%C Theorem: n^n/n! > 2^n/n for n >= 3.

%D D. S. Mitrinovic, Analytic Inequalities, Springer-Verlag, 1970; p. 193, 3.1.21.

%H Harvey P. Dale, <a href="/A127642/b127642.txt">Table of n, a(n) for n = 1..1000</a>

%t Table[Floor[n^n/n!]-Ceiling[2^n/n],{n,40}] (* _Harvey P. Dale_, Jan 09 2016 *)

%K sign

%O 1,4

%A _N. J. A. Sloane_, Apr 03 2007

%E Corrected by _N. J. A. Sloane_, Jan 09 2016, after _Harvey P. Dale_ noticed that something was wrong.

%E More terms from _Harvey P. Dale_, Jan 09 2016