a question about prime trinomials

[Ralf Stephan]

> Also, Jonathan Vos Post and Robert G. Wilson have noted that there are a
> dearth of prime central trinomial coefficients
> http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=A002426
> after n=4.  In fact, I just did a quick check and there are no others
> besides n=2, 3, 4 up to n = 12,000.  

The same appears to be true for the trinomial coefficients in general:
For n<1000, k<=n, A027907(n,k) is prime iff (k=1,n prime) or (2,2),(3,3),(4,4).

Also, GCD(A027907(n,k),n) appears to be >1 for all 1<k<n, and for k==n
if k==0 mod 3 and k/3 is in A074940, which already has an A002426-related
entry.

So, is there a multiplicative formula for A027907?


ralf