a(n) = Sum_{k=1..n} min(k!, binomial(n,k)).

Terms

a(0) =1a(1) =2a(2) =4a(3) =8a(4) =15a(5) =31a(6) =62a(7) =126a(8) =283a(9) =539a(10) =1177a(11) =2459a(12) =4969a(13) =10781a(14) =22297a(15) =45116a(16) =95759a(17) =201615a(18) =400755a(19) =830859a(20) =1741455a(21) =3505627a(22) =7099561a(23) =14607199a(24) =30112789a(25) =60176505a(26) =121626832a(27) =247652036a(28) =504389269a(29) =1010060135