a(n) = (n+1)*(n+2)*(n+3)*(n+4)*(n+15)*3^n/360.

Terms

a(0) =1a(1) =16a(2) =153a(3) =1134a(4) =7182a(5) =40824a(6) =214326a(7) =1058508a(8) =4979799a(9) =22517352a(10) =98513415a(11) =419129802a(12) =1741000716a(13) =7083045648a(14) =28296044604a(15) =111232727064a(16) =431026817373