A127695 Floor( 2*(2*n+1)^n*sinh(1/2) ) - (2*n+2)^n + (2*n)^n.

1, 1, 6, 61, 933, 19013, 486903, 15046084, 545075629, 22661379274, 1063692556445, 55646541997466, 3210791930531340, 202576381691155974, 13874616146693093852, 1025250869305088941530, 81303554487412360191076, 6887348857934410851161581, 620720182437520911247158798

Offset

0,3

Comments

Theorem: 2*(2*n+1)^n*sinh(1/2) > (2*n+2)^n - (2*n)^n for n >= 1.

References

D. S. Mitrinovic, Analytic Inequalities, Springer-Verlag, 1970; p. 192, 3.1.13.

Links

Table of n, a(n) for n=0..18.

Mathematica

Join[{1}, Table[Floor[2(2n+1)^n Sinh[1/2]]-(2n+2)^n+(2n)^n, {n, 20}]] (* Harvey P. Dale, Jun 20 2011 *)

Crossrefs

Sequence in context: A361526 A380039 A056546 * A144343 A022517 A275221

Adjacent sequences: A127692 A127693 A127694 * A127696 A127697 A127698

Keyword

nonn

Author

N. J. A. Sloane, Apr 03 2007

Status

approved