A127696 a(n) = (2*n)^n+(2*n+1)^n-(2*n+2)^n.

1, 1, 5, 47, 657, 12219, 283257, 7837423, 250764161, 9046988147, 359958186777, 15446916156231, 696035549765025, 31596603724765195, 1320452505741997625, 35237128887524220383, -2148849686515840130559, -600767230517127657730077, -91881507441808204259686119

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

Sequence in context: A006902 A367079 A180254 * A088691 A052802 A098799

Adjacent sequences: A127693 A127694 A127695 * A127697 A127698 A127699

Keyword

sign

Author

N. J. A. Sloane, Apr 03 2007

Status

approved