login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A216923 The denominators of Zagier's modification of the Bernoulli numbers. 4
4, 24, 4, 80, 4, 1260, 4, 1120, 4, 264, 4, 12012, 4, 312, 4, 38080, 4, 1220940, 4, 83600, 4, 552, 4, 78936, 4, 24, 4, 30160, 4, 62300700, 4, 2360960, 4, 24, 4, 430666236, 4, 888, 4, 47986400, 4, 202145580, 4, 79120, 4, 1128, 4, 126139728, 4, 264, 4, 4240, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Robert Israel, Table of n, a(n) for n = 1..4655

M. W. Coffey, V. de Angelis, A. Dixit, V. H. Moll, et al., The Zagier polynomials. Part II: Arithmetic properties of coefficients, arXiv:1303.6590 [math.NT], 2013.

Atul Dixit, Victor H. Moll, Christophe Vignat, The Zagier modification of Bernoulli numbers and a polynomial extension. Part I, arXiv:1209.4110v1 [math.NT], 2012.

D. Zagier, A modified Bernoulli number, Nieuw Archief voor Wiskunde, 16:63-72, 1998.

FORMULA

a(n) = denominator(sum_{r=0..n} C(n+r,2*r)*B(r)/(n+r)); B(r) the Bernoulli numbers.

a(n)=4 if n is odd. - Robert Israel, Mar 08 2018

MAPLE

f:= proc(n) if n::odd then 4 else denom(-n/4 + add(binomial(n+r, 2*r)*bernoulli(r)/(n+r), r=0..n, 2)) fi end proc:

map(f, [$1..100]); # Robert Israel, Mar 08 2018

MATHEMATICA

a[n_] := Sum[ Binomial[n + k, 2*k]*BernoulliB[k]/(n + k), {k, 0, n}] // Denominator; Table[a[n], {n, 1, 53}] (* Jean-François Alcover, Jul 26 2013 *)

PROG

(Sage)

def A216923(n):

    return add(binomial(n+r, 2*r)*bernoulli(r)/(n+r) for r in (0..n)).denominator()

[A216923(n) for n in (1..53)]

(PARI) a(n) = denominator(sum(r=0, n, binomial(n+r, 2*r)*bernfrac(r)/(n+r))); \\ Michel Marcus, Aug 05 2018

CROSSREFS

Cf. A216922 (numerators).

Sequence in context: A319145 A024543 A010294 * A233149 A169688 A222595

Adjacent sequences:  A216920 A216921 A216922 * A216924 A216925 A216926

KEYWORD

nonn

AUTHOR

Peter Luschny, Sep 20 2012

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 31 14:49 EDT 2021. Contains 346374 sequences. (Running on oeis4.)