A295231 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.
-4, 15, 765, 61425, 1214325, 95893875, 2615987248875, 298915241625, 10670785663663125, 10218227413637368125, 1605716856726047690625, 56404413605424162403125, 3387648475383059302662121875, 744538093174369303262578125
Offset: 0
Examples
Zeta(2) = Pi^2/6 > 1 + 1/2^2, so Pi^2 > 15/2. Zeta(4) = Pi^4/90 > 1 + 1/2^4, so Pi^4 > 765/8. Zeta(6) = Pi^6/945 > 1 + 1/2^6, so Pi^6 > 61425/64.
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..223
Programs
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PARI
{a(n) = numerator((-1)^(n+1)*(2*n)!*(2^(2*n)+1)/(bernfrac(2*n)*2^(4*n-1)))}
Comments