a(n) = 0^n/2 + 2^n*(n^2+n+2)/4.

Terms

a(0) =1a(1) =2a(2) =8a(3) =28a(4) =88a(5) =256a(6) =704a(7) =1856a(8) =4736a(9) =11776a(10) =28672a(11) =68608a(12) =161792a(13) =376832a(14) =868352a(15) =1982464a(16) =4489216a(17) =10092544a(18) =22544384a(19) =50069504a(20) =110624768a(21) =243269632a(22) =532676608a(23) =1161822208a(24) =2524971008a(25) =5469372416a(26) =11811160064a(27) =25434259456