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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.

%I A335539 #15 Mar 21 2025 04:46:57
%S A335539 1,1,9,1,1350,1,52920,1,1134000,1,11290752,1,74373979680000,1,
%T A335539 8006169600,1,12147360825600000,1,56625794240311296000,1,
%U A335539 3311787858630451200000,1,451287524451778560000,1,48168123888308960600064000000,1,10738530029998374912000000,1
%N 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.
%F A335539 a(n) = denominator(n*Bernoulli(n)*zeta(n)*(4-2^(3-n))/Pi^n) for n >= 2.
%e A335539 Rational sequence starts: 0, 1, 1/9, 0, -7/1350, 0, 31/52920, 0, -127/1134000, 0, 365/11290752, ...
%p A335539 a := s -> `if`(s = 1 or s = 0, s, -4*s^2*Zeta(1 - s)*Zeta(s)*(1 - 2^(1 - s))/Pi^s):
%p A335539 seq(denom(a(s)), s = 0..34);
%Y A335539 Cf. A335538 (numerators), A164555/A027642 (Bernoulli numbers).
%Y A335539 Cf. A335264, A335265, A327497.
%K A335539 nonn,frac
%O A335539 0,3
%A A335539 _Peter Luschny_, Jun 13 2020