Number of self-inverse permutations p on [n] where the maximal displacement of an element equals 3.

Terms

a(0) =0a(1) =0a(2) =0a(3) =0a(4) =2a(5) =7a(6) =19a(7) =47a(8) =117a(9) =284a(10) =675a(11) =1575a(12) =3634a(13) =8312a(14) =18881a(15) =42634a(16) =95797a(17) =214376a(18) =478110a(19) =1063242a(20) =2358703a(21) =5221606a(22) =11538623a(23) =25458412a(24) =56095424a(25) =123458153a(26) =271440387a(27) =596277224a(28) =1308849869a(29) =2871054209