A165226 Numerator of 1 - A164555(n)/A027642(n).

0, 1, 5, 1, 31, 1, 41, 1, 31, 1, 61, 1, 3421, 1, -1, 1, 4127, 1, -43069, 1, 174941, 1, -854375, 1, 236366821, 1, -8553097, 1, 23749461899, 1, -8615841261683, 1, 7709321041727, 1, -2577687858361, 1, 26315271553055396563, 1, -2929993913841553, 1

Offset: 0

Author

Paul Curtz, Sep 09 2009

Keywords

• frac
• easy
• sign

Comments

If n != 1, also the numerator of 1 - Bernoulli(n). The denominators are in A027642.

(There are no common factors to be canceled in the fractions.)

The numerators of 1 - Bernoulli(n) start 0, 3, 5,1, 31, ... and differ only at n=1 from this sequence.

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

Examples

			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
		

Crossrefs

Cf. A162173, A164555, A027642.

Programs

Maple

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

Formula

|a(2n)| = A162173(n+1).

a(2n+1) = 1.