'Mixing number' of permutations

[Edwin Clark]

On Thu, 17 Aug 2006, Brendan McKay wrote:

> 
> The average is  sum(1/binomial(n,k),k=1..n-1).  I don't know
> if this has a closed form or a name.


the sequence n!*sum(1/binomial(n,k),k=1..n-1) is in the OEIS as

  http://www.research.att.com/~njas/sequences/A059371

For what it may be worth Maple simplifies  sum(1/binomial(n,k),k=1..n-1) 
to: 

-1/2*1/n*(n^2*LerchPhi(2,1,n)+2^(-n)*Pi*n^2*I+n+n*LerchPhi(2,1,n)+2^(-n)*Pi*n*I-1)