Number of permutations p of [n] such that 0p has a nonincreasing jump sequence beginning with two.

Terms

a(0) =1a(1) =2a(2) =5a(3) =9a(4) =17a(5) =31a(6) =57a(7) =101a(8) =185a(9) =333a(10) =599a(11) =1089a(12) =1975a(13) =3563a(14) =6505a(15) =11829a(16) =21455a(17) =39257a(18) =71641a(19) =130403a(20) =239193a(21) =437677a(22) =799127a(23) =1468777a(24) =2693853a(25) =4930871a(26) =9079127a(27) =16684737a(28) =30605159a(29) =56441227