A141590 a(n) = numerator of Bernoulli(2*n)/(2*n + 1)!. Bisection of A120082.

1, 1, -1, 1, -1, 1, -691, 1, -3617, 43867, -174611, 77683, -236364091, 657931, -3392780147, 1723168255201, -7709321041217, 151628697551, -26315271553053477373, 154210205991661, -261082718496449122051, 1520097643918070802691, -2530297234481911294093

Offset

0,7

Comments

Numerators of the Taylor expansion coefficients of the Debye function D(1,x) at the even powers of x.

Links

Peter Luschny, Table of n, a(n) for n = 0..300

Kevin Acres and David Broadhurst, Eta quotients and Rademacher sums, arXiv:1810.07478 [math.NT], 2018.

Formula

a(n) = A120082(2*n).

Example

Note that a(34) = -125235502160125163977598011460214000388469 but A255505(34) = -4633713579924631067171126424027918014373353.

Maple

A141590 := proc(n) A120082(2*n) end:
seq(A141590(n), n=0..30) ; # R. J. Mathar, Sep 03 2009
seq(numer(bernoulli(2*n)/(2*n+1)!), n=0..34); # Peter Luschny, Dec 03 2022

Mathematica

Table[Numerator[BernoulliB[2*n]/(2*n+1)!], {n, 0, 35}] (* G. C. Greubel, Sep 16 2024 *)

Prog

(Magma)
A141590:= func< n | Numerator(BernoulliNumber(2*n)/Factorial(2*n+1)) >;
[A141590(n): n in [0..35]]; // G. C. Greubel, Sep 16 2024
(SageMath)
def A141590(n): return numerator(bernoulli(2*n)/factorial(2*n+1))
[A141590(n) for n in range(36)] # G. C. Greubel, Sep 16 2024

Crossrefs

Cf. A000367, A001067, A046968, A120082, A255505.

Sequence in context: A046968 A255505 A001067 * A276594 A283301 A046988

Adjacent sequences: A141587 A141588 A141589 * A141591 A141592 A141593

Keyword

sign,frac

Author

Paul Curtz, Aug 20 2008

Extensions

Edited and extended by R. J. Mathar, Sep 03 2009

Edited by Peter Luschny, Dec 03 2022

Status

approved