asymptotic formula for A006154
Max Alekseyev
maxale at gmail.com
Sun Feb 18 19:47:29 CET 2007
On 2/17/07, Ralf Stephan <ralf at ark.in-berlin.de> wrote:
> > So the entry would be
> >
> > %F A006154 a(n) ~ sqrt(2)/2*(n-1)!/log(1+sqrt(2))^n.
>
> Does someone have or know of a proof?
It should easy follow from the expression of Laurent series
coefficients as contour integrals, and Cauchy integral formula:
http://mathworld.wolfram.com/LaurentSeries.html
http://mathworld.wolfram.com/CauchyIntegralFormula.html
In particular, log(1+sqrt(2)) is a pole for function 1/(1-sinh(x)).
Max
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