Number of permutations of 1..n for which the partial sums of signed displacements do not exceed 2.

Terms

a(0) =1a(1) =1a(2) =2a(3) =6a(4) =12a(5) =25a(6) =57a(7) =124a(8) =268a(9) =588a(10) =1285a(11) =2801a(12) =6118a(13) =13362a(14) =29168a(15) =63685a(16) =139057a(17) =303608a(18) =662888a(19) =1447352a(20) =3160121a(21) =6899745a(22) =15064810a(23) =32892270a(24) =71816436a(25) =156802881a(26) =342360937a(27) =747505396a(28) =1632091412a(29) =3563482500