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

1,1

Links

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

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A002432, A046988.

Sequence in context: A113404 A177283 A121607 * A091800 A336042 A353230

Adjacent sequences: A100591 A100592 A100593 * A100595 A100596 A100597

Keyword

nonn

Author

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

Status

approved