A172457 Numerators of first differences of the sequence A172298(n)/A172282(n).

-5, 5, -1, 1, -1, 1, -1, 1, -1, 25, -25, 477481, -477481, 49, -49, 13082689, -13082689, 1924313689, -1924313689, 30489001321, -30489001321, 730192467169, -730192467169, 55867983514256281, -55867983514256281, 73155570928609

Offset: 0

Author

Paul Curtz, Feb 03 2010

Keywords

• frac
• sign

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.

Crossrefs

Cf. A172298, A172299.

Programs

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