A335539 a(n) = denominator(-4*n^2*zeta(1 - n)*zeta(n)*(1 - 2^(1 - n)) / Pi^n) for n >= 2, a(0) = 1, a(1) = 1.

1, 1, 9, 1, 1350, 1, 52920, 1, 1134000, 1, 11290752, 1, 74373979680000, 1, 8006169600, 1, 12147360825600000, 1, 56625794240311296000, 1, 3311787858630451200000, 1, 451287524451778560000, 1, 48168123888308960600064000000, 1, 10738530029998374912000000, 1

Offset: 0

Author

Peter Luschny, Jun 13 2020

Keywords

• nonn
• frac

Examples

			Rational sequence starts: 0, 1, 1/9, 0, -7/1350, 0, 31/52920, 0, -127/1134000, 0, 365/11290752, ...
		

Crossrefs

Cf. A335538 (numerators), A164555/A027642 (Bernoulli numbers).

Cf. A335264, A335265, A327497.

Programs

Maple

a := s -> `if`(s = 1 or s = 0, s, -4*s^2*Zeta(1 - s)*Zeta(s)*(1 - 2^(1 - s))/Pi^s):
seq(denom(a(s)), s = 0..34);

Formula

a(n) = denominator(n*Bernoulli(n)*zeta(n)*(4-2^(3-n))/Pi^n) for n >= 2.