a(n) = Sum_{d|n} (n/d)^(d-1) * binomial(d+n-2,n-1).

Terms

a(0) =1a(1) =3a(2) =7a(3) =29a(4) =71a(5) =355a(6) =925a(7) =4425a(8) =13276a(9) =60111a(10) =184757a(11) =856357a(12) =2704157a(13) =12137147a(14) =40367461a(15) =176999505a(16) =601080391a(17) =2616894901a(18) =9075135301a(19) =38884056181a(20) =138014377810a(21) =583674491643