a(n)=5a(n-1)+C(n+3,3),n>0, a(0)=1.

Terms

a(0) =1a(1) =9a(2) =55a(3) =295a(4) =1510a(5) =7606a(6) =38114a(7) =190690a(8) =953615a(9) =4768295a(10) =23841761a(11) =119209169a(12) =596046300a(13) =2980232060a(14) =14901160980a(15) =74505805716a(16) =372529029549