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

Author

Paul Curtz, Aug 20 2008

Keywords

• sign
• frac

Comments

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

Examples

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

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.

Crossrefs

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

Programs

Magma

A141590:= func< n | Numerator(BernoulliNumber(2*n)/Factorial(2*n+1)) >;
[A141590(n): n in [0..35]]; // G. C. Greubel, Sep 16 2024

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 *)

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

Formula

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

Extensions

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

Edited by Peter Luschny, Dec 03 2022