a(n) = Sum_{k=0..n} (k+1) * 2^k * binomial(k,n-k)^2.

Terms

a(0) =1a(1) =4a(2) =16a(3) =80a(4) =380a(5) =1760a(6) =8160a(7) =37632a(8) =172560a(9) =788160a(10) =3587712a(11) =16282368a(12) =73704896a(13) =332887040a(14) =1500492800a(15) =6751567872a(16) =30331308288a(17) =136070206464a(18) =609649172480