T(n,k)=Number of idempotent n X n 0..k matrices.

Terms

a(0) =2a(1) =2a(2) =8a(3) =2a(4) =12a(5) =50a(6) =2a(7) =16a(8) =122a(9) =452a(10) =2a(11) =20a(12) =218a(13) =2052a(14) =5682a(15) =2a(16) =24a(17) =344a(18) =5584a(19) =54182a(20) =96608a(21) =2a(22) =28a(23) =488a(24) =12476a(25) =248442a(26) =2236302a(27) =2185738a(28) =2a(29) =32