A127425 Floor((n*(n+1)^3/8)^n)-(n!)^4.

0, 0, 29, 12528, 14927013, 44632974375, 289553896419667, 3621335176611561472, 79763800168579144103361, 2886490238072828615188093125, 162510049064391484117789761805165, 13624190843866457706897020192739557376, 1640800492737366435568874082163705520197134

Offset: 0

Author

N. J. A. Sloane, Apr 02 2007

Keywords

• nonn

Comments

Theorem: (n*(n+1)^3/8)^n > (n!)^4 for n > 1.

Examples

			(n*(n+1)^3/8)^n - (n!)^4 gives 0, 0, 473/16, 12528, 238832209/16, 44632974375, 1186012759734957321/4096, ...
		

References

• D. S. Mitrinovic, Analytic Inequalities, Springer-Verlag, 1970; p. 193, 3.1.17.

Programs

Mathematica

Join[{0},Array[Floor[(#(#+1)^3/8)^#-(#!)^4]&,12]] (* James C. McMahon, Dec 31 2024 *)