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A127695 Floor( 2*(2*n+1)^n*sinh(1/2) ) - (2*n+2)^n + (2*n)^n. 0
1, 1, 6, 61, 933, 19013, 486903, 15046084, 545075629, 22661379274, 1063692556445, 55646541997466, 3210791930531340, 202576381691155974, 13874616146693093852, 1025250869305088941530, 81303554487412360191076, 6887348857934410851161581, 620720182437520911247158798 (list; graph; refs; listen; history; text; internal format)
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: A049120 A271841 A056546 * A144343 A022517 A275221

Adjacent sequences:  A127692 A127693 A127694 * A127696 A127697 A127698

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Apr 03 2007

STATUS

approved

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Last modified September 25 21:33 EDT 2017. Contains 292500 sequences.