cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A100594 #15 May 29 2017 03:17:07
%S A100594 6,90,945,9450,93555,924041,9121612,90030844,888579011,8769948429,
%T A100594 86555983552,854273468992,8431341566236,83214006759229,
%U A100594 821289329637860,8105800788023426,80001047145799660,789578687036411293
%N A100594 Floor of Pi^(2*n)/Zeta(2*n).
%H A100594 Vincenzo Librandi, <a href="/A100594/b100594.txt">Table of n, a(n) for n = 1..200</a>
%e A100594 a(1)=6 because Zeta(2*1)=Pi^2/6 implies Pi^2/Zeta(2)=6 and floor(6)=6.
%e A100594 a(6)=924041 because Zeta(2*6)=691/638512875*Pi^12 implies Pi^12/Zeta(12)=638512875/691 and floor(638512875/691)=924041.
%p A100594 seq(simplify(floor(Pi^(2*k)/Zeta(2*k))),k=1..24);
%t A100594 Table[Floor[Pi^(2*n)/Zeta[2*n]],{n,20}] (* _Terry D. Grant_, May 28 2017 *)
%o A100594 (PARI) {a(n)=if(n<1, 0, floor(-2*(2*n)!/(-4)^n/bernfrac(2*n)))} /* _Michael Somos_, Feb 18 2007 */
%Y A100594 Cf. A002432, A046988.
%K A100594 nonn
%O A100594 1,1
%A A100594 Joseph Biberstine (jrbibers(AT)indiana.edu), Nov 30 2004