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%I #13 Aug 08 2017 05:04:17
%S 0,1,5,1,31,1,41,1,31,1,61,1,3421,1,-1,1,4127,1,-43069,1,174941,1,
%T -854375,1,236366821,1,-8553097,1,23749461899,1,-8615841261683,1,
%U 7709321041727,1,-2577687858361,1,26315271553055396563,1,-2929993913841553,1
%N Numerator of 1 - A164555(n)/A027642(n).
%C If n != 1, also the numerator of 1 - Bernoulli(n). The denominators are in A027642.
%C (There are no common factors to be canceled in the fractions.)
%C The numerators of 1 - Bernoulli(n) start 0, 3, 5,1, 31, ... and differ only at n=1 from this sequence.
%C E.g.f. for the rationals r(n) = a(n)/A027642(n) = 1 - A164555(n)/A027642(n): exp(x)*(1 - x/(exp(x) - 1)). - _Wolfdieter Lang_, Aug 07 2017
%F |a(2n)| = A162173(n+1).
%F a(2n+1) = 1.
%e The rationals r(n) begin: 0, 1/2, 5/6, 1, 31/30, 1, 41/42, 1, 31/30, 1, 61/66, 1, 3421/2730, 1, -1/6, 1, 4127/510, 1, -43069/798, 1, ... - _Wolfdieter Lang_, Aug 07 2017
%p A165226 := proc(n) if n = 1 then 1+bernoulli(n) ; else 1-bernoulli(n) ; end if; numer(%) ; end proc: # _R. J. Mathar_, Jan 16 2011
%Y Cf. A162173, A164555, A027642.
%K frac,easy,sign
%O 0,3
%A _Paul Curtz_, Sep 09 2009
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