cp's OEIS Frontend

A176150 Numerators of the inverse binomial transform of a shuffled sequence of "original" Bernoulli and Bernoulli numbers.

%I A176150 #9 Apr 22 2021 16:32:31
%S A176150 1,0,-1,0,13,-20,14,-73,373,-776,196,-223,1027,-1956,242,139,-3521,
%T A176150 2288,-824,-36433,600283,-502708,83638,-40071,4098793,1096584,
%U A176150 -1160948,3484553,-6256069,4889852,-1520674,-276156781
%N A176150 Numerators of the inverse binomial transform of a shuffled sequence of "original" Bernoulli and Bernoulli numbers.
%C A176150 Define a shuffled sequence bb1(n) by taking the "original" Bernoulli numbers for even indices and the Bernoulli numbers for odd indices: bb1(2n) = A164555(n)/A027642(n), bb1(2n+1) = A027641(n)/A027642(n).
%C A176150 This starts bb1(n) = 1, 1, 1/2, -1/2, 1/6, 1/6, 0, 0, -1/30, -1/30, 0, 0, 1/42, 1/42,...
%C A176150 The inverse binomial transform of bb1(n) starts 1, 0, -1/2, 0, 13/6, -20/3, 14, -73/3 and its numerators define the current sequence.
%p A176150 bb1 := proc(n)
%p A176150     nh := floor(n/2) ;
%p A176150     if n <= 1 then
%p A176150         bernoulli(nh) ;
%p A176150     elif n <= 3 then
%p A176150         -(-1)^n*bernoulli(nh) ;
%p A176150     else
%p A176150         bernoulli(nh) ;
%p A176150     end if;
%p A176150 end proc:
%p A176150 [seq(bb1(n),n=0..40)] ;
%p A176150 read("transforms");
%p A176150 BINOMIALi(%) ;
%p A176150 numer(%) ; # _R. J. Mathar_, Mar 26 2013
%K A176150 frac,sign,uned
%O A176150 0,5
%A A176150 _Paul Curtz_, Apr 10 2010, Apr 19 2010