A127634 a(n) = 3^(n-1) - ceiling(n^n/n!).

0, 1, 4, 16, 54, 178, 565, 1770, 5493, 16927, 51901, 158533, 482802, 1466859, 4448104, 13467249, 40720970, 122994566, 371156622, 1119161662, 3372427789, 10156591942, 30573367574, 91993546765, 276703494365, 832023918335, 2501142914874, 7516883840470

Offset: 1

Author

N. J. A. Sloane, Apr 03 2007

Keywords

• nonn

Comments

Theorem: 3^(n-1) > n^n/n! for n >= 3.

References

• D. S. Mitrinovic, Analytic Inequalities, Springer-Verlag, 1970; p. 193, 3.1.21.

Links

• Robert Israel, Table of n, a(n) for n = 1..2094

Crossrefs

Cf. A000244, A073225.

Programs

Magma

[3^(n-1)-Ceiling(n^n/Factorial(n)): n in [1..30]]; // Vincenzo Librandi, Jul 06 2017

Maple

seq(3^(n-1)-ceil(n^n/n!),n=1..50); # Robert Israel, Jul 06 2017

Mathematica

Table[3^(n-1) - Ceiling[n^n / n!], {n, 30}] (* Vincenzo Librandi, Jul 06 2017 *)

PARI

a(n) = 3^(n-1) - ceil(n^n/n!); \\ Michel Marcus, Jul 06 2017