a(n) = [x^n] exp(Sum_{k>=1} x^k*(1 + (n - 3)*x^k)/(k*(1 - x^k)^3)).

Terms

a(0) =1a(1) =1a(2) =3a(3) =10a(4) =40a(5) =150a(6) =616a(7) =2456a(8) =10102a(9) =41400a(10) =171526a(11) =712111a(12) =2972115a(13) =12434993a(14) =52195414a(15) =219567909a(16) =925704792a(17) =3909841659a(18) =16541598215a(19) =70085877919a(20) =297347922785