G.f.: Sum_{n>=0} x^n * (1+x)^(n*(n+1)/2) / Product_{k=1..n} (1 + x*(1+x)^k).

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =2a(5) =3a(6) =7a(7) =15a(8) =38a(9) =102a(10) =291a(11) =894a(12) =2881a(13) =9814a(14) =35049a(15) =130827a(16) =509444a(17) =2062695a(18) =8667549a(19) =37723094a(20) =169735610a(21) =788356105a(22) =3774150884a(23) =18599067832a(24) =94236062123a(25) =490360221092