OFFSET
0,1
COMMENTS
The sequence A172298(n)/A172282(n) = 1, -1/4, 1/36, 0, 1/900, 0, 1/1764, 0, 1/900, 0, 25/4356, ... contains (up to a sign flip of the element at n=1) the squares of the Bernoulli numbers.
The first differences if this sequence of fractions are -5/4, 5/18, -1/36, 1/900, -1/900, 1/1764, -1/1764, 1/900, -1/900, ...
The sequence contains the numerators of these first differences.
MAPLE
Bsq := proc(n)
if n =1 then
-bernoulli(n)^2 ;
else
bernoulli(n)^2 ;
end if;
end proc:
B := [seq(Bsq(n), n=0..30)] ;
read("transforms"); DIFF(B) ;
apply(numer, %) ; # R. J. Mathar, Jul 13 2011
CROSSREFS
KEYWORD
frac,sign
AUTHOR
Paul Curtz, Feb 03 2010
STATUS
approved