Number of permutations of [n] whose lengths of increasing runs are distinct squares.

Terms

a(0) =1a(1) =1a(2) =0a(3) =0a(4) =1a(5) =8a(6) =0a(7) =0a(8) =0a(9) =1a(10) =18a(11) =0a(12) =0a(13) =1428a(14) =47998a(15) =0a(16) =1a(17) =32a(18) =0a(19) =0a(20) =9688a(21) =505056a(22) =0a(23) =0a(24) =0a(25) =4085949a(26) =284958912a(27) =0a(28) =0a(29) =290824632172