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 A256003 #23 Jul 01 2015 18:01:42 %S A256003 0,2,0,1,0,-1,0,1,0,-1,0,5,0,-691,0,7,0,-3617,0,43867,0,-174611,0, %T A256003 854513,0,-236364091,0,8553103,0,-23749461029,0,8615841276005,0, %U A256003 -7709321041217,0,2577687858367,0,-26315271553053477373,0 %N A256003 a(n) = 0 followed by numerators of 2*A176327(n)/A176289(n). %C A256003 Offset 0 is chosen instead of -1. (The offset 0 corresponds to A176327(n), -1 to 0 followed by A176327(n).) %C A256003 Denominators: b(n) = 1 followed by A141459(n). %C A256003 Difference table of a(n)/b(n): %C A256003 0, 2, 0, 1/3, 0, -1/15, 0, ... %C A256003 2, -2, 1/3, -1/3, -1/15, 1/15, ... %C A256003 -4, 7/3, -2/3, 4/15, 2/15, ... %C A256003 19/3, -3, 14/15, -2/15, ... %C A256003 -28/3, 59/15, -16/15, ... %C A256003 199/15, -5, ... %C A256003 -274/15, ... %C A256003 etc. %C A256003 Without the first column, the antidiagonal sums are (-1)^n * A254667(n+1). %C A256003 The Bernoulli numbers A027641(n)/A027642(n) or A164555(n)/A027642(n) come from A000027. 0 followed by the Bernoulli numbers comes from A001477. a(0)=0 is a choice. %F A256003 a(2n) = 0. a(2n+1) = A172086(2n), from the main pure Bernoulli twin numbers. %Y A256003 Cf. A176327/A176289, A172086/A172087, A141459, A176618, A195240, A254667. %K A256003 sign,frac %O A256003 0,2 %A A256003 _Paul Curtz_, May 06 2015