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

Terms

a(0) =1a(1) =0a(2) =2a(3) =3a(4) =16a(5) =30a(6) =252a(7) =399a(8) =4672a(9) =8100a(10) =111200a(11) =193006a(12) =3279888a(13) =5631093a(14) =114137072a(15) =196030350a(16) =4600308224a(17) =7873377297a(18) =210745840824a(19) =359490499457