asymptotic formula for A006154

[Simon Plouffe]

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
1/(1-sinh(x)).

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
Inverter.

Simon Plouffe