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

Terms

a(0) =1a(1) =1a(2) =3a(3) =9a(4) =31a(5) =125a(6) =579a(7) =3009a(8) =17255a(9) =108005a(10) =731883a(11) =5331625a(12) =41501135a(13) =343405709a(14) =3007557523a(15) =27775308049a(16) =269603741111