a(n) = n*2^(n-1) + binomial(n,2)*2^(n-2) + binomial(n,3)*2^(n-3).

Terms

a(0) =0a(1) =1a(2) =5a(3) =19a(4) =64a(5) =200a(6) =592a(7) =1680a(8) =4608a(9) =12288a(10) =32000a(11) =81664a(12) =204800a(13) =505856a(14) =1232896a(15) =2969600a(16) =7077888a(17) =16711680a(18) =39124992a(19) =90898432a(20) =209715200a(21) =480772096a(22) =1095761920a(23) =2484076544a(24) =5603590144a(25) =12582912000a(26) =28135391232a(27) =62662901760a(28) =139049566208a(29) =307492814848