A172282 -id:A172282 - cp's OEIS frontend

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

Paul Curtz, Feb 03 2010

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.

Cf. A172298, A172299.

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

A172298 a(n) = A027641(n) * A164555(n).

Original entry on oeis.org

1, -1, 1, 0, 1, 0, 1, 0, 1, 0, 25, 0, 477481, 0, 49, 0, 13082689, 0, 1924313689, 0, 30489001321, 0, 730192467169, 0, 55867983514256281, 0, 73155570928609, 0, 564036899167989738841, 0, 74232720893311466588760025, 0, 59433630916551169012841089, 0, 6644474695172651051906689

Offset: 0

Paul Curtz, Jan 31 2010

sign

Squares of Bernoulli number numerators (apart from the sign flipped at a(1)).

The associated denominators of the squared Bernoulli numbers are in A172282.

Cf. A027641, A164555, A172282.

Edited and extended by R. J. Mathar, Feb 02 2010

cp's OEIS Frontend

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

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