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

Terms

a(0) =1a(1) =2a(2) =8a(3) =35a(4) =164a(5) =787a(6) =3857a(7) =19147a(8) =96004a(9) =485009a(10) =2465013a(11) =12589315a(12) =64555985a(13) =332158127a(14) =1714001409a(15) =8866730665a(16) =45968787524a(17) =238778897128