G.f.: Sum_{n>=0} x^n * Sum_{k=0..n} C(n,k) * ((1+x)^k - 1)^k.

Terms

a(0) =1a(1) =1a(2) =2a(3) =3a(4) =8a(5) =21a(6) =70a(7) =263a(8) =1072a(9) =4842a(10) =23351a(11) =120478a(12) =660372a(13) =3817413a(14) =23213642a(15) =147866712a(16) =983535760a(17) =6814069842a(18) =49050260795a(19) =366092901787