Triangle T(n,k) of ways n couples can sit in a row with exactly k of them together.

Terms

a(0) =1a(1) =0a(2) =2a(3) =8a(4) =8a(5) =8a(6) =240a(7) =288a(8) =144a(9) =48a(10) =13824a(11) =15744a(12) =8064a(13) =2304a(14) =384a(15) =1263360a(16) =1401600a(17) =710400a(18) =211200a(19) =38400a(20) =3840a(21) =168422400a(22) =183582720a(23) =92620800a(24) =28108800a(25) =5529600a(26) =691200a(27) =46080a(28) =30865121280a(29) =33223034880