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

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

Offset

0,3

Comments

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

References

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

Links

Table of n, a(n) for n=0..12.

Example

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

Mathematica

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

Crossrefs

Sequence in context: A201489 A028459 A199369 * A135253 A262715 A274545

Adjacent sequences: A127422 A127423 A127424 * A127426 A127427 A127428

Keyword

nonn

Author

N. J. A. Sloane, Apr 02 2007

Status

approved