a(n) = T(n, 3), where T(n, k) = Sum_{i=0..n} i^k * binomial(n, i) * (1/2)^(n-k).

Terms

a(0) =0a(1) =4a(2) =20a(3) =54a(4) =112a(5) =200a(6) =324a(7) =490a(8) =704a(9) =972a(10) =1300a(11) =1694a(12) =2160a(13) =2704a(14) =3332a(15) =4050a(16) =4864a(17) =5780a(18) =6804a(19) =7942a(20) =9200a(21) =10584a(22) =12100a(23) =13754a(24) =15552a(25) =17500a(26) =19604a(27) =21870a(28) =24304a(29) =26912