G.f. for a(n) = C(2n,n)*Sum_{k=0..2n} T(n,k)/C(2n,k) ?

[Paul D. Hanna]

Max (and Seqfans),
      Thanks, Max.  Not as simple as I wished, but at least it 
has a finite expression - good work.  
  
BTW, it seems that the OEIS has been down for a while ... 
does anyone know when it will be back up? 
 
Does this mean that the Seqfan email server is down also? 
Thanks, 
      Paul 
 
On Sat, 18 Aug 2007 11:57:37 -0700 "Max Alekseyev" <maxale at gmail.com>
writes:
> I've got the following o.g.f. for a(n) but I was not able to simplify 
> it much:
> 
> SUM a(n) * t^n =
> 
> (1+sqrt(1-4*t)) * (-b+sqrt(b^2-4*c)) / sqrt(1-4*t) / ( 8*t*c - 
> 2*b^2*t
> + b^2 + b^2*sqrt(1-4*t) + 2*b*t*sqrt(b^2-4*c) - b*sqrt(b^2-4*c) -
> b*sqrt((b^2-4*c)*(1-4*t)) - b - b*sqrt(1-4*t) - 2*c - 
> 2*sqrt(1-4*t)*c
> + sqrt(b^2-4*c) + sqrt((b^2-4*c)*(1-4*t)) )
> 
> +
> 
> (1+sqrt(1-4*t*c)) * (-b+sqrt(b^2-4*c)) / sqrt(1-4*t*c) / ( 2*b^2*t 
> -
> 2*b*t*sqrt(b^2-4*c) - 8*t*c - b - b*sqrt(1-4*t*c) + sqrt(b^2-4*c) +
> sqrt((b^2-4*c)*(1-4*t*c)) + 2 + 2*sqrt(1-4*t*c) )
> 
> Regards,
> Max