d(n,s) = number of perfect matchings on {1, 2, ..., n} with s short pairs.

Terms

a(0) =1a(1) =0a(2) =1a(3) =1a(4) =1a(5) =1a(6) =5a(7) =6a(8) =3a(9) =1a(10) =36a(11) =41a(12) =21a(13) =6a(14) =1a(15) =329a(16) =365a(17) =185a(18) =55a(19) =10a(20) =1a(21) =3655a(22) =3984a(23) =2010a(24) =610a(25) =120a(26) =15a(27) =1a(28) =47844a(29) =51499