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

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =5a(5) =11a(6) =33a(7) =108a(8) =357a(9) =1405a(10) =5713a(11) =24670a(12) =117413a(13) =574007a(14) =3004577a(15) =16608120a(16) =95057925a(17) =576245913a(18) =3622049809a(19) =23693870554a(20) =161816447365