From the game of Mousetrap.

Terms

a(0) =1a(1) =0a(2) =2a(3) =6a(4) =31a(5) =180a(6) =1255a(7) =9949a(8) =89162a(9) =886837a(10) =9722814a(11) =116236256a(12) =1507191024a(13) =21042127239