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

Terms

a(0) =1a(1) =1a(2) =3a(3) =9a(4) =25a(5) =71a(6) =198a(7) =543a(8) =1486a(9) =4045a(10) =11007a(11) =29931a(12) =81371a(13) =221197a(14) =601294a(15) =1634497a(16) =4443046a(17) =12077467a(18) =32829975a(19) =89241140a(20) =242582583a(21) =659407855a(22) =1792456409a(23) =4872401706a(24) =13244561047a(25) =36002449653a(26) =97864804698a(27) =266024120284a(28) =723128532126