a(n) = (n*4^(n+1) + (6*4^(n+1)+(-1)^n)/5)/5.

Terms

a(0) =1a(1) =7a(2) =41a(3) =215a(4) =1065a(5) =5079a(6) =23593a(7) =107479a(8) =482345a(9) =2139095a(10) =9395241a(11) =40936407a(12) =177167401a(13) =762356695a(14) =3264175145a(15) =13915694039a(16) =59098749993a(17) =250138895319