a(n) = Sum_{k=0..floor(n/2)} C(n-k,k)^5.

Terms

a(0) =1a(1) =1a(2) =2a(3) =33a(4) =245a(5) =1268a(6) =10903a(7) =108801a(8) =876184a(9) =7319995a(10) =70550669a(11) =663827604a(12) =6051592703a(13) =57695451167a(14) =563736086740