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

0,1

Comments

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

Links

Seiichi Manyama, Table of n, a(n) for n = 0..223

Example

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.

Prog

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

Crossrefs

Cf. A002432/A046988, A295232 (denominators).

Sequence in context: A006524 A299683 A341598 * A070037 A297859 A298127

Adjacent sequences: A295228 A295229 A295230 * A295232 A295233 A295234

Keyword

sign,frac

Author

Seiichi Manyama, Nov 18 2017

Status

approved