a(n) = (n - 1/3)*2^n - n/2 + 1/4 + (-1)^n/12.

Terms

a(0) =1a(1) =6a(2) =20a(3) =57a(4) =147a(5) =360a(6) =850a(7) =1959a(8) =4433a(9) =9894a(10) =21840a(11) =47781a(12) =103759a(13) =223908a(14) =480590a(15) =1026723a(16) =2184525a(17) =4631202a(18) =9786700a(19) =20621985a(20) =43341131a(21) =90876576a(22) =190141770a(23) =397060767a(24) =827675977a(25) =1722460830a(26) =3579139400a(27) =7426714269a(28) =15390299463