a(n) = 6^n*(n^2 - n + 72)/72.

Terms

a(0) =1a(1) =6a(2) =37a(3) =234a(4) =1512a(5) =9936a(6) =66096a(7) =443232a(8) =2985984a(9) =20155392a(10) =136048896a(11) =917070336a(12) =6167549952a(13) =41358864384a(14) =276451356672