a(n) = 4^n * Sum_{i=1..n} i^4/4^i.

Terms

a(0) =1a(1) =20a(2) =161a(3) =900a(4) =4225a(5) =18196a(6) =75185a(7) =304836a(8) =1225905a(9) =4913620a(10) =19669121a(11) =78697220a(12) =314817441a(13) =1259308180a(14) =5037283345a(15) =20149198916a(16) =80596879185a(17) =322387621716