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 A260196 #42 Dec 24 2018 03:25:30 %S A260196 1,-3,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1, %T A260196 -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1, %U A260196 -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1 %N A260196 1, -3, followed by -1's. %C A260196 1/(n+1) is the inverse Akiyama-Tanigawa transform of A164555(n)/A027642(n). %C A260196 For more on the Akiyama-Tanigawa transform, see Links (correction: page 7 read here A164555 instead of A027641) and A177427. %C A260196 Here: %C A260196 1, -3, -1, -1, -1, -1, ... %C A260196 4, -4, 0, 0, 0, 0, ... %C A260196 8, -8, 0, 0, 0, 0, ... %C A260196 16, -16, 0, 0, 0, 0, ... %C A260196 etc. %C A260196 Other process, using signed A130534(n), different of A008275(n): %C A260196 1, 1/1, 1, %C A260196 1, 4, ( 1, -1)/1, -3, %C A260196 1, 4, 8, ( 2, -3, 1)/2, -1, %C A260196 1, 4, 8, 16, * ( 6, -11, 6, -1)/6, = -1, %C A260196 1, 4, 8, 16, 32, ( 24, -50, 35, -10, 1)/24, -1, %C A260196 1, 4, 8, 16, 32, 64, (120, -274, 225, -85, 15, -1)/120, -1, %C A260196 etc. etc. etc. %C A260196 Via the modified Stirling numbers of the first kind, the second triangle, Iw(n), is the inverse of Worpitzky transform A163626(n). %C A260196 a(n) is the third sequence of a family beginning with %C A260196 1, 1, 1, 1, 1, 1, 1, 1, ... = A000012(n) %C A260196 1, 0, 0, 0, 0, 0, 0, 0, 0, ... = A000007(n) %C A260196 1, -3, -1, -1, -1, -1, -1, -1, -1, -1, ... . %C A260196 A000012(n) is the inverse Akiyama-Tanigawa transform of A000007(n), with or without its second term. %C A260196 A000007(n) is the inverse Akiyama-Tanigawa transform of A000012(n), with or without its second term. %C A260196 a(n) is the inverse Akiyama-Tanigawa transform of 2^n omitting the second term i.e. 2. %H A260196 Colin Barker, <a href="/A260196/b260196.txt">Table of n, a(n) for n = 0..1000</a> %H A260196 Masanobu Kaneko, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL3/KANEKO/AT-kaneko.html">The Akiyama-Tanigawa algorithm for Bernoulli numbers</a>, Journal of Integer Sequences, 3(2000), article 00.2.9 %H A260196 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1). %F A260196 Inverse Akiyama-Tanigawa transform of A151821(n). %F A260196 From _Colin Barker_, Sep 11 2015: (Start) %F A260196 a(n) = -1 for n>1. %F A260196 a(n) = a(n-1) for n>2. %F A260196 G.f.: -(2*x^2-4*x+1) / (x-1). %F A260196 (End) %o A260196 (PARI) first(m)=vector(m,i,i--;if(i>1,-1,if(i==0,1,if(i==1,-3)))) \\ _Anders Hellström_, Aug 28 2015 %o A260196 (PARI) Vec(-(2*x^2-4*x+1)/(x-1) + O(x^100)) \\ _Colin Barker_, Sep 11 2015 %Y A260196 Cf. A000007, A000012, A008275, A027642, A130534, A151821, A163626, A164555, A177427. %K A260196 sign,easy %O A260196 0,2 %A A260196 _Paul Curtz_, Jul 19 2015