OFFSET
0,3
COMMENTS
Theorem: (2*n)^n > (2*n+1)^n + (2*n+2)^n for 1 <= n <= 15.
REFERENCES
D. S. Mitrinovic, Analytic Inequalities, Springer-Verlag, 1970; p. 192, 3.1.13.
LINKS
Robert Israel, Table of n, a(n) for n = 0..351
FORMULA
a(n) = (2*n)^n*(1+sqrt(e)-e + O(1/n)) as n -> infinity. - Robert Israel, Feb 16 2018
MAPLE
f:= n -> (2*n)^n+(2*n+1)^n-(2*n+2)^n:
map(f, [$0..30]); # Robert Israel, Feb 16 2018
CROSSREFS
KEYWORD
sign
AUTHOR
N. J. A. Sloane, Apr 03 2007
STATUS
approved