lattice path counting

[Brendan McKay]

Here is a summation for it.  Not as efficient as the recurrences,
but maybe useful for something.   Maple code follows.

> f := proc(n) local i,k;
>    add(add((-1)^k*binomial(k,i)*(-1)^i*binomial(i,n)^3,i=n..k),k=n..3*n)
> end:
>
> seq(f(n),n=0..6);
        1, 13, 409, 16081, 699121, 32193253, 1538743249

Brendan.