asking for help in connection with a new sequence

[Paul D. Hanna]

Sorry, when I typed: 
> Further, a formula for term T(2n+m-1,n), m>=0, (by inspection) is: 
> T(2n+3m),n+m) =  (2n+3m+1)/(3m+1) * [x^n] GF006605(x)^(3m+1)
 
it should have been:
 
Further, a formula for term T(2n+3m,n+m), m>=0, (by inspection) is:  
 
T(2n+3m,n+m) =  (2n+3m+1)/(3m+1) * [x^n] GF006605(x)^(3m+1)
 
But I think that this was clear from the examples. 
    Paul