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a(n) = numerator(4^(n + 1)*zeta(-n, 1/4)).
1

%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