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.

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).

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%I A276595 #32 Jul 15 2018 13:49:17
%S A276595 24,1440,60480,2419200,95800320,2615348736000,149448499200,
%T A276595 21341245685760000,10218188434341888000,1605715325396582400000,
%U A276595 28202200078783610880000,3387648273463487338905600000,372269041039943663616000000,75786531374911731038945280000000
%N 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).
%C A276595 Denominator of Bernoulli(2*n)/(2*(2*n)!). - _Robert Israel_, Sep 18 2016
%H A276595 Robert Israel, <a href="/A276595/b276595.txt">Table of n, a(n) for n = 1..223</a>
%F A276595 A276592(n)/A276593(n) + A276594(n)/a(n) = A046988(n)/A002432(n).
%F A276595 Zeta(2n) = (-1)^(n-1)*(A276594(n)/a(n))*((2*Pi)^(2n)), according to Euler. - _Terry D. Grant_, Jun 19 2018
%p A276595 seq(denom(sum(1/(2*k)^(2*n),k=1..infinity)/Pi^(2*n)),n=1..24);
%p A276595 seq(denom(bernoulli(2*n)/2/(2*n)!),n=1..24); # _Robert Israel_, Sep 18 2016
%t A276595 Table[Denominator[Zeta[2*n]/(2*Pi)^(2*n)], {n, 1, 30}] (* _Terry D. Grant_, Jun 19 2018 *)
%o A276595 (PARI) a(n) = denominator(bernfrac(2*n)/(2*(2*n)!)); \\ _Michel Marcus_, Jul 05 2018
%Y A276595 Cf. A002432, A046988, A276592, A276593, A276594.
%K A276595 nonn,frac
%O A276595 1,1
%A A276595 _Martin Renner_, Sep 07 2016