>  nops(V4);
                                       9

>  add(vpw(V4[i]),i=1..nops(V4));
                                       1

> 
>  # There are 9 vector partitions of 4 with crank = 4 mod 5
>  # and total weight = 1.
> 

==============================================================================

 We see that

 NV(0,5,4)=NV(1,5,4)=NV(2,5,4)=NV(3,5,4)=NV(4,5,4)=1=p(4)/5