a(n) = Sum_{k=0..n} (-3)^(n-k) * binomial(2*n+1,k).

Terms

a(0) =1a(1) =0a(2) =4a(3) =8a(4) =36a(5) =120a(6) =456a(7) =1680a(8) =6340a(9) =23960a(10) =91224a(11) =348656a(12) =1337896a(13) =5149872a(14) =19877904a(15) =76907808a(16) =298176516a(17) =1158168792a(18) =4505865144a(19) =17555689008a(20) =68490100536a(21) =267518448912