asymptotic formula for A006154

Simon Plouffe simon.plouffe at
Sat Feb 17 03:56:45 CET 2007

Hello Neil and seqfan.

  I have computed a formula for A006154.

a(n) ~ sqrt(2)/2*(n-1)!/log(1+sqrt(2))^n

a(100) is about 162 digits long and the approximation is good to 56
digits. This is the principal term in the asymptotic expansion
of the n'th term in the series expansion of

So the entry would be

%F A006154 a(n) ~ sqrt(2)/2*(n-1)!/log(1+sqrt(2))^n.

In this case, I could not use <equivalent> of Salvy because
of the singularity, but of course numerically this is
a workable example, the log(1+sqrt(2))^n part was found using the

Simon Plouffe

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