[seqfan] Re: Guess the Triangle

[William Keith]

> T(n,k)=Number of idempotent nXn 0..k matrices of rank n-1
>
> Rows n=1..6 match
> a(k) = 1
> a(k) = 4*k + 2
> a(k) = 6*k^2 + 12*k + 3
> a(k) = 8*k^3 + 24*k^2 + 24*k + 4
> a(k) = 10*k^4 + 40*k^3 + 60*k^2 + 40*k + 5
> a(k) = 12*k^5 + 60*k^4 + 120*k^3 + 120*k^2 + 60*k + 6

Pascal's triangle times 2n, except for the last coefficient, which is
just times n.

William Keith