a(n)=2*a(n-1)+(n+3)*a(n-2)-(n+3)*a(n-3), a(0)=0, a(1)=0, a(2)=1.

Terms

a(0) =0a(1) =0a(2) =1a(3) =2a(4) =11a(5) =30a(6) =141a(7) =472a(8) =2165a(9) =8302a(10) =38613a(11) =163144a(12) =780953a(13) =3554402a(14) =17611557a(15) =85145196a(16) =437376337a(17) =2225425454a(18) =11847704869a(19) =63032490312a(20) =347377407169