%I #7 Jul 09 2021 14:58:49
%S 1,1,-1,-7,5,31,-61,-127,1385,511,-50521,-1414477,2702765,8191,
%T -199360981,-118518239,19391512145,5749691557,-2404879675441,
%U -91546277357,370371188237525,162912981133,-69348874393137901,-1982765468311237,15514534163557086905,22076500342261
%N a(n) = numerator(4^(n + 1)*zeta(-n, 1/4)).
%F a(n)/A344918(n) - 2*A092440(n)*zeta(-n) = -A163982(n) for n >= 0.
%e Rational sequence starts: 1, 1/6, -1, -7/60, 5, 31/126, -61, -127/120, 1385, ...
%p seq(numer(4^(n+1)*Zeta(0, -n, 1/4)), n=0..25);
%o (SageMath)
%o def a(n): return 4^(n+1)*hurwitz_zeta(-n, 1/4) if n > 0 else 1
%o print([a(n).numerator() for n in (0..25)])
%Y Cf. A344918 (denominators), A092440, A163982.
%K sign,frac
%O 0,4
%A _Peter Luschny_, Jul 09 2021