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

Terms

a(0) =1a(1) =1a(2) =1a(3) =4a(4) =0a(5) =0a(6) =1a(7) =12a(8) =54a(9) =1002a(10) =0a(11) =0a(12) =0a(13) =0a(14) =0a(15) =0a(16) =0a(17) =0a(18) =0a(19) =0a(20) =0a(21) =0a(22) =0a(23) =0a(24) =1a(25) =48a(26) =648a(27) =39444a(28) =0a(29) =0