a(n) = Sum_{k=0..floor(n/2)} k*binomial(n,2*k) = floor(n*2^(n-3)).

Terms

a(0) =0a(1) =0a(2) =1a(3) =3a(4) =8a(5) =20a(6) =48a(7) =112a(8) =256a(9) =576a(10) =1280a(11) =2816a(12) =6144a(13) =13312a(14) =28672a(15) =61440a(16) =131072a(17) =278528a(18) =589824a(19) =1245184a(20) =2621440a(21) =5505024a(22) =11534336a(23) =24117248a(24) =50331648a(25) =104857600a(26) =218103808a(27) =452984832a(28) =939524096a(29) =1946157056