a(n) is the number of shallow permutations of length n that avoid 231.

Terms

a(0) =1a(1) =1a(2) =2a(3) =5a(4) =14a(5) =41a(6) =121a(7) =355a(8) =1037a(9) =3025a(10) =8824a(11) =25746a(12) =75130a(13) =219246a(14) =639805a(15) =1867066a(16) =5448412a(17) =15899370a(18) =46397015a(19) =135394275a(20) =395103258a(21) =1152977744a(22) =3364582879a(23) =9818418346a(24) =28651794889a(25) =83610752932a(26) =243990229487a(27) =712004497223