A261813 Decimal expansion of (Pi/4)^N*(N^N/N!)^2 for N = 3.

9, 8, 1, 0, 5, 7, 9, 7, 3, 0, 8, 7, 6, 1, 1, 4, 9, 7, 7, 3, 9, 6, 8, 0, 2, 8, 1, 4, 2, 0, 0, 0, 5, 0, 8, 2, 5, 7, 0, 4, 0, 9, 5, 2, 1, 0, 2, 9, 9, 5, 8, 4, 8, 5, 6, 3, 5, 0, 4, 2, 0, 2, 5, 9, 4, 0, 7, 4, 9, 2, 1, 4, 1, 8, 5, 4, 3, 8, 3, 5, 5, 0, 9, 4, 8, 8, 3, 8, 9, 9, 8, 5, 9, 7, 0, 0, 6, 9, 5, 9, 5, 1, 3, 4, 3

Offset: 1

Author

Stanislav Sykora, Nov 19 2015

Keywords

• nonn
• cons

Comments

The general expression is a lower bound (due to H. Minkowski) on the discriminant of a number field of degree N.

The corresponding value for N = 2 matches A091476.

Examples

			9.8105797308761149773968028142000508257040952102995848563504202594...
		

References

• B. Mazur, Algebraic Numbers, in The Princeton Companion to Mathematics, Editor T. Gowers, Princeton University Press, 2008, Section IV.1, page 330.

Links

• Stanislav Sykora, Table of n, a(n) for n = 1..2000

Crossrefs

Cf. A000796, A091476 (N=2).

Programs

Mathematica

n = 3; First@ RealDigits[N[(Pi/4)^n (n^n/n!)^2, 120]] (* Michael De Vlieger, Nov 19 2015 *)

PARI

N=3;(Pi/4)^N*(N^N/N!)^2

Formula

Equals 81*Pi^3/256.