Triangle T(n,k) = number of degree-n permutations with k even cycles, k=0..n.

Terms

a(0) =1a(1) =1a(2) =0a(3) =1a(4) =1a(5) =0a(6) =3a(7) =3a(8) =0a(9) =0a(10) =9a(11) =12a(12) =3a(13) =0a(14) =0a(15) =45a(16) =60a(17) =15a(18) =0a(19) =0a(20) =0a(21) =225a(22) =345a(23) =135a(24) =15a(25) =0a(26) =0a(27) =0a(28) =1575a(29) =2415