a(n)=5a(n-1)+C(n+4,4),n>0, a(0)=1.

Terms

a(0) =1a(1) =10a(2) =65a(3) =360a(4) =1870a(5) =9476a(6) =47590a(7) =238280a(8) =1191895a(9) =5960190a(10) =29801951a(11) =149011120a(12) =745057420a(13) =3725289480a(14) =18626450460a(15) =93132256176a(16) =465661285725