login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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). 4
24, 1440, 60480, 2419200, 95800320, 2615348736000, 149448499200, 21341245685760000, 10218188434341888000, 1605715325396582400000, 28202200078783610880000, 3387648273463487338905600000, 372269041039943663616000000, 75786531374911731038945280000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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

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

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 *)

PROG

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

CROSSREFS

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

Sequence in context: A269271 A347857 A187852 * A348700 A010797 A260784

Adjacent sequences:  A276592 A276593 A276594 * A276596 A276597 A276598

KEYWORD

nonn,frac

AUTHOR

Martin Renner, Sep 07 2016

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 25 19:19 EDT 2022. Contains 354071 sequences. (Running on oeis4.)