bit of editing wanted : are these equivalent?

[wouter meeussen]

a spot of trouble:

both my
Numerators of Series[1/(1 + Cosh[Sqrt[x]]), {x, 0, 24}]
and Benoit's
Numerators of  ...  2/(exp(x)+1)
are equivalent,

but DIFFERENT from

Numerators of Table[2*BernoulliB[2*n]*(4^n - 1)/(2*n), {n, 25}]
that, (saving Benoit's day), correctly gives the
Denominators of Pi^(2n)/(Gamma[2n]*(1 - 2^(-2n))*Zeta[2n])

Close, but no cigar,
'cause the ratios between latter and former are:

{1,1,1,1,1,1,1,1,1,1,1,17,1,1,1,1,1,1,1,527,1,1,1,1,31}
differences for n= 11,19 and 24 (offset 0)

does that ring a Bell?
a Bernoulli-effect?

W.

----- Original Message -----
From: "Brendan McKay" <bdm at cs.anu.edu.au>
To: <seqfan at ext.jussieu.fr>
Sent: Saturday, December 06, 2003 11:03 PM
Subject: Re: bit of editing wanted : are these equivalent?


> * benoit <abcloitre at wanadoo.fr> [031207 08:56]:
> >
> > Yes that's an interesting equivalence. Let (A(n)) having g.f.
> > x/(1+cosh(x)) and (B(n))  having g.f. 2/(1+exp(x))
> >
> > then A(n)+n*B(n)=0
>
> x times the derivative of 2/(1+exp(x)) is the negative of x/(1+cosh(x)),
> that's all.
>
> B.
>
>
>