|
|
A176150
|
|
Numerators of the inverse binomial transform of a shuffled sequence of "original" Bernoulli and Bernoulli numbers.
|
|
3
|
|
|
1, 0, -1, 0, 13, -20, 14, -73, 373, -776, 196, -223, 1027, -1956, 242, 139, -3521, 2288, -824, -36433, 600283, -502708, 83638, -40071, 4098793, 1096584, -1160948, 3484553, -6256069, 4889852, -1520674, -276156781
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,5
|
|
COMMENTS
|
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).
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,...
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.
|
|
LINKS
|
|
|
MAPLE
|
bb1 := proc(n)
nh := floor(n/2) ;
if n <= 1 then
bernoulli(nh) ;
elif n <= 3 then
-(-1)^n*bernoulli(nh) ;
else
bernoulli(nh) ;
end if;
end proc:
[seq(bb1(n), n=0..40)] ;
read("transforms");
BINOMIALi(%) ;
|
|
CROSSREFS
|
|
|
KEYWORD
|
frac,sign,uned
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|