a(n) = n*2^(2*n-2) + n*binomial(2*n,n)/2.

Terms

a(0) =0a(1) =2a(2) =14a(3) =78a(4) =396a(5) =1910a(6) =8916a(7) =40684a(8) =182552a(9) =808614a(10) =3545220a(11) =15414212a(12) =66556584a(13) =285707708a(14) =1220340296a(15) =5189913240a(16) =21988512304a(17) =92850096902a(18) =390913863012