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

1,1

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.

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

Formula

Equals 81*Pi^3/256.

Example

9.8105797308761149773968028142000508257040952102995848563504202594...

Mathematica

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

Prog

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

Crossrefs

Cf. A000796, A091476 (N=2).

Sequence in context: A232737 A155683 A343469 * A198920 A354593 A244115

Adjacent sequences: A261810 A261811 A261812 * A261814 A261815 A261816

Keyword

nonn,cons

Author

Stanislav Sykora, Nov 19 2015

Status

approved