%I #10 Mar 26 2013 18:19:54
%S 1,1,-1,1,1,1,0,0,-1,-1,0,0,1,1,0,0,-1,-1,0,0,5,5,0,0,-691,-691,0,0,7,
%T 7,0,0,-3617,-3617,0,0
%N a(2n) = A027641(n). a(2n+1) = A164555(n).
%C Essentially the same as A176144. (The signs of the third and fourth entry are swapped.)
%C This refers to a shuffling of the "original" Bernoulli numbers and the Bernoulli numbers in opposite order compared to the composition discussed in A176150.
%C The inverse binomial transform of the shuffle in A176150 was 1,0, -1/2, 0, 13/6, -20/3. The shuffling here would yield an inverse binomial transform 1, 0, -3/2, 4, -47/6, 40/3, -21, 95/3 etc.
%C The difference between the corresponding elements of these two binomial transforms element by element is 0, 0, 1, -4, 10, -20, 35, -56, 84, -120, 165, -220,..., a signed variant of A000292.
%K frac,less,sign
%O 0,21
%A _Paul Curtz_, Apr 11 2010