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 A172170 #10 Mar 31 2012 20:35:59
%S A172170 1,1,1,3,3,5,5,7,7,3,3,11,11,13,13,3,3,17,17,19,19,3,3,23,23,5,5,3,3,
%T A172170 29,29,31,31,3,3,5,5,37,37,3,3,41,41,43,43,3,3,47,47,7,7,3,3,53,53,5,
%U A172170 5,3,3,59,59,61,61,3,3,5,5,67,67,3,3,71,71,73,73,3,3,7,7,79,79,3,3,83,83,5,5
%N A172170 1 followed by the duplicated entries of A090368.
%C A172170 We start from the expansion tan(x)+sec(x) = sum_{n>=1} A099612(n)/A099617(n) * x^n with Taylor coefficients 1, 1, 1/2, 1/3, 5/24, 2/15,...
%C A172170 The first differences of this sequence of fractions are 0, -1/2, -1/6, -1/8, -3/40, -7/144, -31/1008, -113/5760,... which is 0 followed by the negated ratios A034428(n)/(n+1)! = 0, -1/2, -1/6, -3/24, -9/120,....
%C A172170 (The factorial follows because A034428 is obtained by multiplying with 1-x to generate first differences of the o.g.f. and then moving on to the e.g.f.)
%C A172170 The common multiple to reduce numerator and denominator of A034428(n)/A000142(n+1) to the standard coprime representation is this sequence here.
%F A172170 a(2n+1)=a(2n+2) = A090368(n), n>=0.
%K A172170 nonn
%O A172170 0,4
%A A172170 _Paul Curtz_, Jan 28 2010