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

Terms

a(0) =1a(1) =1a(2) =4a(3) =14a(4) =52a(5) =193a(6) =724a(7) =2736a(8) =10404a(9) =39759a(10) =152555a(11) =587323a(12) =2267578a(13) =8776197a(14) =34038411a(15) =132262696a(16) =514774705a(17) =2006461961a(18) =7830924282a(19) =30599035846a(20) =119692591204a(21) =468651774760