A100594 Floor of Pi^(2*n)/Zeta(2*n).

6, 90, 945, 9450, 93555, 924041, 9121612, 90030844, 888579011, 8769948429, 86555983552, 854273468992, 8431341566236, 83214006759229, 821289329637860, 8105800788023426, 80001047145799660, 789578687036411293

Offset: 1

Author

Joseph Biberstine (jrbibers(AT)indiana.edu), Nov 30 2004

Keywords

• nonn

Examples

			a(1)=6 because Zeta(2*1)=Pi^2/6 implies Pi^2/Zeta(2)=6 and floor(6)=6.
a(6)=924041 because Zeta(2*6)=691/638512875*Pi^12 implies Pi^12/Zeta(12)=638512875/691 and floor(638512875/691)=924041.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A002432, A046988.

Programs

Maple

seq(simplify(floor(Pi^(2*k)/Zeta(2*k))),k=1..24);

Mathematica

Table[Floor[Pi^(2*n)/Zeta[2*n]],{n,20}] (* Terry D. Grant, May 28 2017 *)

PARI

{a(n)=if(n<1, 0, floor(-2*(2*n)!/(-4)^n/bernfrac(2*n)))} /* Michael Somos, Feb 18 2007 */