A106458 - OEIS

%I #26 Sep 29 2024 19:28:31

%S 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,

%T 0,6,0,870,0,14322,0,510,0,6,0,1919190,0,6,0,13530,0,1806,0,690,0,282,

%U 0,46410,0,66,0,1590,0,798,0,870,0,354,0,56786730

%N Bernoulli number denominators, with zeros at the odd places.

%C A027642 is the correct version of this sequence. - _N. J. A. Sloane_

%C 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

%D 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

%H Antti Karttunen, <a href="/A106458/b106458.txt">Table of n, a(n) for n = 0..16384</a>

%F 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.

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

%t a[n_] := If[OddQ[n] && n>2, 0, BernoulliB[n] // Denominator]; Table[a[n],{n,0,60}] (* _Jean-François Alcover_, Dec 29 2012 *)

%t Join[{1,2},Riffle[BernoulliB[2*Range[50]]//Denominator,0]] (* _Harvey P. Dale_, Sep 29 2024 *)

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

%Y Cf. A027642, A006954, A007318.

%Y Cf. A159688. - _Gary W. Adamson_, Apr 19 2009

%K nonn,frac

%O 0,2

%A _Gary W. Adamson_, May 02 2005

%E Typo in one term corrected by _Paul Curtz_, Jul 16 2008