Third column of PE^4.

Terms

a(0) =0a(1) =0a(2) =1a(3) =12a(4) =120a(5) =1160a(6) =11340a(7) =113988a(8) =1185968a(9) =12802896a(10) =143475300a(11) =1668342060a(12) =20111265768a(13) =251047344600