A295231 - OEIS

%I #21 Nov 18 2017 13:13:47

%S -4,15,765,61425,1214325,95893875,2615987248875,298915241625,

%T 10670785663663125,10218227413637368125,1605716856726047690625,

%U 56404413605424162403125,3387648475383059302662121875,744538093174369303262578125

%N Numerators of (-1)^(n+1) * (2*n)! * (2^(2*n)+1)/(B_{2*n} * 2^(4*n-1)), where B_{n} is the Bernoulli number.

%C Pi^(2*n) > a(n)/A295232(n) for n > 0.

%H Seiichi Manyama, <a href="/A295231/b295231.txt">Table of n, a(n) for n = 0..223</a>

%e Zeta(2) = Pi^2/6   > 1 + 1/2^2, so Pi^2 >    15/2.

%e Zeta(4) = Pi^4/90  > 1 + 1/2^4, so Pi^4 >   765/8.

%e Zeta(6) = Pi^6/945 > 1 + 1/2^6, so Pi^6 > 61425/64.

%o (PARI) {a(n) = numerator((-1)^(n+1)*(2*n)!*(2^(2*n)+1)/(bernfrac(2*n)*2^(4*n-1)))}

%Y Cf. A002432/A046988, A295232 (denominators).

%K sign,frac

%O 0,1

%A _Seiichi Manyama_, Nov 18 2017