A340243 a(n) = denominator((2*n-1)*zeta(2*n)/Pi^(2*n)).

2, 6, 30, 189, 1350, 10395, 58046625, 1403325, 21709437750, 2292899734125, 80596287646875, 640374140030625, 8779111824511153125, 443779279041223125, 20913098524817639765625, 195202717402382161174828125, 2015813566807172297008593750, 367589532770719654160390625

Offset

0,1

Comments

For numerators a(n+1) see A046988.

Links

Table of n, a(n) for n=0..17.

Formula

a(n) = denominator((2*n-1)*2^(2*n-1)*Bernoulli(2*n)/(2*n)!). - Peter Luschny, Jan 12 2021

Example

1/2, 1/6, 1/30, 1/189, 1/1350, 1/10395, 691/58046625, 2/1403325, 3617/21709437750, 43867/2292899734125, ...

Maple

a := n -> denom((2*n-1)*Zeta(2*n)/Pi^(2*n));
seq(a(n), n=0..17); # Peter Luschny, Jan 12 2021

Mathematica

Denominator[Table[(2 n - 1)*Zeta[2 n]/Pi^(2 n), {n, 0, 16}]]

Prog

(PARI) a(n) = denominator((2*n-1)*2^(2*n-1)*bernfrac(2*n)/(2*n)!); \\ Michel Marcus, Jun 15 2022

Crossrefs

Cf. A002432, A027642, A046988, A176289, A164555.

Sequence in context: A195154 A353995 A353982 * A078700 A176719 A203000

Adjacent sequences: A340240 A340241 A340242 * A340244 A340245 A340246

Keyword

nonn,frac

Author

Artur Jasinski, Jan 01 2021

Status

approved