Table by antidiagonals of number of ways of choosing k items from n*k.

Terms

a(0) =1a(1) =1a(2) =2a(3) =1a(4) =6a(5) =3a(6) =1a(7) =20a(8) =15a(9) =4a(10) =1a(11) =70a(12) =84a(13) =28a(14) =5a(15) =1a(16) =252a(17) =495a(18) =220a(19) =45a(20) =6a(21) =1a(22) =924a(23) =3003a(24) =1820a(25) =455a(26) =66a(27) =7a(28) =1a(29) =3432