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Denominators of eta(2*n)/Pi^(2*n), where eta(n) is the Dirichlet eta function.
2

%I #5 Oct 15 2013 10:56:45

%S 2,12,720,30240,1209600,6842880,1307674368000,74724249600,

%T 1524374691840000,5109094217170944000,802857662698291200000,

%U 287777551824322560000,1693824136731743669452800000,186134520519971831808000000

%N Denominators of eta(2*n)/Pi^(2*n), where eta(n) is the Dirichlet eta function.

%C The first 5 terms of this sequence are the same as in A060055.

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Dirichlet_eta_function">Dirichlet eta function</a>

%H Index entries for <a href="/index/Be#Bernoulli">Bernoulli numbers</a> B(2n)

%F a(n) = A036280(n)*Pi^(2*n)/(zeta(2*n)*(1 - 2^(1-2*n))).

%F a(n) = denominator((-1)^(n+1)*BernoulliB(2*n)*(2^(2*n-1) - 1)/(2*n)!).

%F a(n) = 2*A036281(n).

%o (PARI) for(n=0, 7, print1(2*denominator(polcoeff(Ser(1/sin(x)), 2*n-1)), ", "));

%Y Numerators give A036280.

%K nonn,easy,frac

%O 0,1

%A _Arkadiusz Wesolowski_, Oct 14 2013