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

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =3a(5) =5a(6) =9a(7) =16a(8) =31a(9) =61a(10) =125a(11) =266a(12) =579a(13) =1305a(14) =3009a(15) =7120a(16) =17255a(17) =42697a(18) =108005a(19) =278466a(20) =731883a(21) =1958589a(22) =5331625a(23) =14758720a(24) =41501135a(25) =118507301a(26) =343405709a(27) =1009313322a(28) =3007557523a(29) =9081204849