a(n) = 4!*n*Stirling2(n-1,4).

Terms

a(0) =0a(1) =0a(2) =0a(3) =0a(4) =0a(5) =120a(6) =1440a(7) =10920a(8) =67200a(9) =367416a(10) =1864800a(11) =9003720a(12) =41976000a(13) =190788312a(14) =850930080a(15) =3741028200a(16) =16264684800a(17) =70093951608a(18) =299953709280