A127610 a(n) = floor(( (n+1)/2 )^n) - n!.

0, 0, 0, 2, 15, 123, 1118, 11344, 127831, 1590245, 21700716, 322880256, 5209007463, 90661989607, 1694616510154, 33876697720832, 721588072472639, 16321494271570569, 390811944752490542, 9878354899591168000, 262896868506265373394, 7349159002086450661211

Offset: 0

Author

N. J. A. Sloane, Apr 03 2007

Keywords

• nonn

Comments

Theorem (Cauchy): ((n+1)/2)^n > n! for n >= 2.

References

• D. S. Mitrinovic, Analytic Inequalities, Springer-Verlag, 1970; p. 192, 3.1.14.

Links

• Paolo Xausa, Table of n, a(n) for n = 0..420

Crossrefs

Cf. A127426.

Programs

Mathematica

A127610[n_] := Floor[((n+1)/2)^n] - n!;
Array[A127610, 25, 0] (* Paolo Xausa, Jan 29 2024 *)