a(n) = [x^n] Product_{k=1..n} 1/(1 - x^k)^(n-k+1).

Terms

a(0) =1a(1) =1a(2) =4a(3) =17a(4) =80a(5) =384a(6) =1887a(7) =9385a(8) =47139a(9) =238488a(10) =1213588a(11) =6204547a(12) =31844710a(13) =163978344a(14) =846741721a(15) =4382945317a(16) =22735196277a(17) =118151632006a(18) =615032941924