This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A335538 #12 Mar 21 2025 04:47:25 %S A335538 0,1,1,0,-7,0,31,0,-127,0,365,0,-977403607,0,57337,0,-61240067209,0, %T A335538 252221719530919,0,-15984987035583127,0,2841046127487821,0, %U A335538 -468654557583574838590567,0,188822581306893585883,0,-220710643004244238794643249,0,1594135539680034434970146279285311 %N A335538 a(n) = numerator(-4*n^2*zeta(1 - n)*zeta(n)*(1 - 2^(1 - n)) / Pi^n) for n >= 2, a(0) = 0, a(1) = 1. %F A335538 a(n) = numerator(n*Bernoulli(n)*zeta(n)*(4-2^(3-n))/Pi^n) for n >= 2. %e A335538 Rational sequence starts: 0, 1, 1/9, 0, -7/1350, 0, 31/52920, 0, -127/1134000, 0, 365/11290752, ... %p A335538 a := s -> `if`(s=1 or s=0, s, -4*s^2*Zeta(1 - s)*Zeta(s)*(1 - 2^(1 - s)) / Pi^s): %p A335538 seq(numer(a(s)), s = 0..34); %Y A335538 Cf. A335539 (denominators), A164555/A027642 (Bernoulli numbers). %Y A335538 Cf. A335264, A335265, A327497. %K A335538 sign,frac %O A335538 0,5 %A A335538 _Peter Luschny_, Jun 13 2020