A276595 Denominator of the rational part of the sum of reciprocals of even powers of even numbers, i.e., Sum_{k>=1} 1/(2*k)^(2*n).

24, 1440, 60480, 2419200, 95800320, 2615348736000, 149448499200, 21341245685760000, 10218188434341888000, 1605715325396582400000, 28202200078783610880000, 3387648273463487338905600000, 372269041039943663616000000, 75786531374911731038945280000000

Offset: 1

Author

Martin Renner, Sep 07 2016

Keywords

• nonn
• frac

Comments

Denominator of Bernoulli(2*n)/(2*(2*n)!). - Robert Israel, Sep 18 2016

Links

• Robert Israel, Table of n, a(n) for n = 1..223

Crossrefs

Cf. A002432, A046988, A276592, A276593, A276594.

Programs

Maple

seq(denom(sum(1/(2*k)^(2*n),k=1..infinity)/Pi^(2*n)),n=1..24);
seq(denom(bernoulli(2*n)/2/(2*n)!),n=1..24); # Robert Israel, Sep 18 2016

Mathematica

Table[Denominator[Zeta[2*n]/(2*Pi)^(2*n)], {n, 1, 30}] (* Terry D. Grant, Jun 19 2018 *)

PARI

a(n) = denominator(bernfrac(2*n)/(2*(2*n)!)); \\ Michel Marcus, Jul 05 2018

Formula

A276592(n)/A276593(n) + A276594(n)/a(n) = A046988(n)/A002432(n).

Zeta(2n) = (-1)^(n-1)*(A276594(n)/a(n))*((2*Pi)^(2n)), according to Euler. - Terry D. Grant, Jun 19 2018