A106458 Bernoulli number denominators, with zeros at the odd places.

1, 2, 6, 0, 30, 0, 42, 0, 30, 0, 66, 0, 2730, 0, 6, 0, 510, 0, 798, 0, 330, 0, 138, 0, 2730, 0, 6, 0, 870, 0, 14322, 0, 510, 0, 6, 0, 1919190, 0, 6, 0, 13530, 0, 1806, 0, 690, 0, 282, 0, 46410, 0, 66, 0, 1590, 0, 798, 0, 870, 0, 354, 0, 56786730

Offset: 0

Author

Gary W. Adamson, May 02 2005

Keywords

• nonn
• frac

Comments

A027642 is the correct version of this sequence. - N. J. A. Sloane

Equals right border of triangle A159688 if zeros are inserted in A159688 to allow for (n+1) terms per row. - Gary W. Adamson, Apr 19 2009

Examples

			Solutions to the system of simultaneous equations with 5 rows: (-1/2, 1/6, 0, -1/30, 0).
		

References

• Robert M. Young, "Excursions in Calculus" MAA, 1992, p. 91 J. H. Conway & R. K. Guy, "The Book of Numbers", Springer-Verlag, 1996, p. 108

Links

• Antti Karttunen, Table of n, a(n) for n = 0..16384

Crossrefs

Cf. A027642, A006954, A007318.

Cf. A159688. - Gary W. Adamson, Apr 19 2009

Programs

Mathematica

a[n_] := If[OddQ[n] && n>2, 0, BernoulliB[n] // Denominator]; Table[a[n],{n,0,60}] (* Jean-François Alcover, Dec 29 2012 *)
Join[{1,2},Riffle[BernoulliB[2*Range[50]]//Denominator,0]] (* Harvey P. Dale, Sep 29 2024 *)

PARI

A106458(n) = if((n%2)&&n>1,0,denominator(bernfrac(n))); \\ Antti Karttunen, Dec 19 2018

Formula

In addition to generating functions as shown in A006954, the Bernoulli numbers starting with B(1) = -1/2 may be generated from the following system of simultaneous equations: (exemplified by 5 rows): 2 0 0 0 0 = -1 3 3 0 0 0 = -1 4 6 4 0 0 = -1 5 10 10 5 0 = -1 6 15 20 15 6 = -1.

Extensions

Typo in one term corrected by Paul Curtz, Jul 16 2008