This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A165226 #13 Aug 08 2017 05:04:17 %S A165226 0,1,5,1,31,1,41,1,31,1,61,1,3421,1,-1,1,4127,1,-43069,1,174941,1, %T A165226 -854375,1,236366821,1,-8553097,1,23749461899,1,-8615841261683,1, %U A165226 7709321041727,1,-2577687858361,1,26315271553055396563,1,-2929993913841553,1 %N A165226 Numerator of 1 - A164555(n)/A027642(n). %C A165226 If n != 1, also the numerator of 1 - Bernoulli(n). The denominators are in A027642. %C A165226 (There are no common factors to be canceled in the fractions.) %C A165226 The numerators of 1 - Bernoulli(n) start 0, 3, 5,1, 31, ... and differ only at n=1 from this sequence. %C A165226 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 A165226 |a(2n)| = A162173(n+1). %F A165226 a(2n+1) = 1. %e A165226 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 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 A165226 Cf. A162173, A164555, A027642. %K A165226 frac,easy,sign %O A165226 0,3 %A A165226 _Paul Curtz_, Sep 09 2009