A295232 Denominator of (-1)^(n+1) * (2*n)! * (2^(2*n)+1)/(B_{2*n} * 2^(4*n-1)), where B_{n} is the Bernoulli number.

1, 2, 8, 64, 128, 1024, 2830336, 32768, 118521856, 11499470848, 183092903936, 651652235264, 3965531409350656, 88306004000768, 1821484971735384064, 7400951301593676906496, 16555640873195841519616, 2604961188466481168384

Offset

0,2

Comments

Pi^(2*n) > A295231(n)/a(n) for n > 0.

Links

Seiichi Manyama, Table of n, a(n) for n = 0..275

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) = denominator((-1)^(n+1)*(2*n)!*(2^(2*n)+1)/(bernfrac(2*n)*2^(4*n-1)))}

Crossrefs

Cf. A002432/A046988, A295231 (numerators).

Sequence in context: A153554 A139018 A110708 * A287229 A323853 A354276

Adjacent sequences: A295229 A295230 A295231 * A295233 A295234 A295235

Keyword

nonn,frac

Author

Seiichi Manyama, Nov 18 2017

Status

approved