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

0,2

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

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

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.

Example

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

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 *)

Prog

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

Crossrefs

Cf. A027642, A006954, A007318.

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

Sequence in context: A285119 A202535 A138703 * A354351 A213323 A293016

Adjacent sequences: A106455 A106456 A106457 * A106459 A106460 A106461

Keyword

nonn,frac,changed

Author

Gary W. Adamson, May 02 2005

Extensions

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

Status

approved