T(n,k) is the number of singly defective permutations of 1..n+2*k-2 with exactly k maxima.

Terms

a(0) =0a(1) =3a(2) =2a(3) =120a(4) =80a(5) =15a(6) =4760a(7) =3552a(8) =860a(9) =64a(10) =249984a(11) =199168a(12) =57064a(13) =6576a(14) =220a(15) =17512704a(16) =14548480a(17) =4643712a(18) =681984a(19) =42112a(20) =672a(21) =1599330304a(22) =1367568384a(23) =469942528a(24) =80506880a(25) =6849792a(26) =242688a(27) =1904a(28) =185616337920a(29) =162107703296