Number of parity preserving permutations of the set {1,2,...,n} with exactly k cycles.

Terms

a(0) =1a(1) =0a(2) =1a(3) =0a(4) =1a(5) =1a(6) =0a(7) =1a(8) =2a(9) =1a(10) =0a(11) =2a(12) =5a(13) =4a(14) =1a(15) =0a(16) =4a(17) =12a(18) =13a(19) =6a(20) =1a(21) =0a(22) =12a(23) =40a(24) =51a(25) =31a(26) =9a(27) =1a(28) =0a(29) =36