A230265 Denominators of eta(2*n)/Pi^(2*n), where eta(n) is the Dirichlet eta function.

2, 12, 720, 30240, 1209600, 6842880, 1307674368000, 74724249600, 1524374691840000, 5109094217170944000, 802857662698291200000, 287777551824322560000, 1693824136731743669452800000, 186134520519971831808000000

Offset: 0

Author

Arkadiusz Wesolowski, Oct 14 2013

Keywords

• nonn
• easy
• frac

Comments

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

Links

• Wikipedia, Dirichlet eta function
• Index entries for Bernoulli numbers B(2n)

Crossrefs

Numerators give A036280.

Programs

PARI

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

Formula

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

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

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