a(n) = (1/4) * Sum_{k=0..floor(n/2)} (k+2) * 2^k * binomial(2*k+2,2*n-4*k+1).

Terms

a(0) =1a(1) =0a(2) =6a(3) =6a(4) =24a(5) =80a(6) =104a(7) =560a(8) =800a(9) =2960a(10) =6720a(11) =15200a(12) =46384a(13) =90944a(14) =273184a(15) =601248a(16) =1525760a(17) =3863552a(18) =8808192a(19) =23230464a(20) =53175296a(21) =134251008a(22) =323028992a(23) =774392832a(24) =1920513280a(25) =4529858560a(26) =11176308224a(27) =26669133312a(28) =64509908992a(29) =156109492224