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

Terms

a(0) =1a(1) =3a(2) =11a(3) =44a(4) =189a(5) =880a(6) =4542a(7) =26712a(8) =182793a(9) =1461368a(10) =13477650a(11) =140564536a(12) =1627370146a(13) =20621925504a(14) =283161372284