A172298 -id:A172298 - cp's OEIS frontend

A172299 First differences of A172298.

-2, 2, -1, 1, -1, 1, -1, 1, -1, 25, -25, 477481, -477481, 49, -49, 13082689, -13082689, 1924313689, -1924313689, 30489001321, -30489001321, 730192467169, -730192467169, 55867983514256281, -55867983514256281, 73155570928609, -73155570928609

Offset: 0

Paul Curtz, Jan 31 2010

sign

Differences between squares of Bernoulli number denominators.

a(n) = A172298(n+1)-A172298(n).

a(2n) = -a(2n-1), n>=2 .

Keyword:sign added, sequence extended by R. J. Mathar, Feb 02 2010

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

Original entry on oeis.org

-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

A172282 Squares of Bernoulli number denominators A027642.

Original entry on oeis.org

1, 4, 36, 1, 900, 1, 1764, 1, 900, 1, 4356, 1, 7452900, 1, 36, 1, 260100, 1, 636804, 1, 108900, 1, 19044, 1, 7452900, 1, 36, 1, 756900, 1, 205119684, 1, 260100, 1, 36, 1, 3683290256100, 1, 36, 1, 183060900, 1, 3261636, 1, 476100, 1, 79524, 1, 2153888100, 1, 4356, 1, 2528100

Offset: 0

Paul Curtz, Jan 30 2010

Compare the sequence for example with A120083.

Antti Karttunen, Table of n, a(n) for n = 0..4096

Cf. A120083, A172298.

Denominator[BernoulliB[Range[0,60]]]^2 (* Harvey P. Dale, Sep 26 2024 *)

A172282(n) = (denominator(bernfrac(n))^2); \\ Antti Karttunen, Dec 19 2018

a(n) = A027642(n)^2 .

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

cp's OEIS Frontend

A172299 First differences of A172298.

Views

Author

Keywords

Comments

Formula

Extensions

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

Views

Author

Keywords

Comments

Crossrefs

Programs

Maple

A172282 Squares of Bernoulli number denominators A027642.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

Formula

Extensions