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