A344917 a(n) = numerator(4^(n + 1)*zeta(-n, 1/4)).

1, 1, -1, -7, 5, 31, -61, -127, 1385, 511, -50521, -1414477, 2702765, 8191, -199360981, -118518239, 19391512145, 5749691557, -2404879675441, -91546277357, 370371188237525, 162912981133, -69348874393137901, -1982765468311237, 15514534163557086905, 22076500342261

Offset: 0

Author

Peter Luschny, Jul 09 2021

Keywords

• sign
• frac

Examples

			Rational sequence starts: 1, 1/6, -1, -7/60, 5, 31/126, -61, -127/120, 1385, ...
		

Crossrefs

Cf. A344918 (denominators), A092440, A163982.

Programs

Maple

seq(numer(4^(n+1)*Zeta(0, -n, 1/4)), n=0..25);

SageMath

def a(n): return 4^(n+1)*hurwitz_zeta(-n, 1/4) if n > 0 else 1
print([a(n).numerator() for n in (0..25)])

Formula

a(n)/A344918(n) - 2*A092440(n)*zeta(-n) = -A163982(n) for n >= 0.