a(n) = floor(n^m) where m = Sum_{k=1..n} (1/k).

Terms

a(0) =1a(1) =2a(2) =7a(3) =17a(4) =39a(5) =80a(6) =155a(7) =284a(8) =500a(9) =849a(10) =1395a(11) =2233a(12) =3487a(13) =5329a(14) =7989a(15) =11770a(16) =17068a(17) =24395a(18) =34410a(19) =47947a(20) =66063a(21) =90080a(22) =121643a(23) =162787a(24) =216013a(25) =284381a(26) =371612a(27) =482210a(28) =621605a(29) =796306