OFFSET
0,4
COMMENTS
The array of (-1)^n*A176328(n)/A176591(n) and its first, second, etc. differences in subsequence rows starts as follows:
1, 1, 7/6, 3/2, 59/30, 5/2, 127/42, ... see A176328,
0, 1/6, 1/3, 7/15, 8/15, 11/21, 10/21, ...
1/6, 1/6, 2/15, 1/15, -1/105, -1/21, -1/105, ... see A190339
0, -1/30, -1/15, -8/105, -4/105, 4/105, -116/1155, ...
The numerators in the 3rd row, 0, 1/6, 1/3, 7/15, 8/15, 11/21, 10/21, 7/15, 8/15, 19/33, 14/33, 337/1365, 1028/1365, 5/3, -2/3, -1681/255, 1936/255, ... define the current sequence.
The associated denominators are 1, 6 and followed by 3, 15, 15 etc as provided in A172087.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..300
MAPLE
read("transforms") ;
evb := [0, 1, 0, seq(bernoulli(n), n=2..30)] ;
ievb := BINOMIALi(evb) ;
[seq((-1)^n*op(n, ievb), n=1..nops(ievb))] ;
DIFF(%) ;
DIFF(%) ;
apply(numer, %) ; # R. J. Mathar, Sep 20 2011
MATHEMATICA
evb = Join[{0, 1, 0}, Table[BernoulliB[n], {n, 2, 32}]]; ievb = Table[ Sum[Binomial[n, k]*evb[[k+1]], {k, 0, n}], {n, 0, Length[evb]-3}]; Differences[ievb, 2] // Numerator (* Jean-François Alcover, Sep 09 2013, after R. J. Mathar *)
CROSSREFS
KEYWORD
sign,frac
AUTHOR
Paul Curtz, Sep 13 2011
STATUS
approved