Sum_{k=0..n} (n-k)^(2*k).

Terms

a(0) =1a(1) =1a(2) =2a(3) =6a(4) =27a(5) =163a(6) =1268a(7) =12344a(8) =145653a(9) =2036149a(10) =33192790a(11) =622384730a(12) =13263528351a(13) =318121600695