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

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =3a(5) =6a(6) =12a(7) =25a(8) =54a(9) =120a(10) =278a(11) =666a(12) =1671a(13) =4355a(14) =11804a(15) =33019a(16) =94960a(17) =279219a(18) =836907a(19) =2550991a(20) =7901818a(21) =24875931a(22) =79667065a(23) =259892494a(24) =864832484a(25) =2938862050a(26) =10204420451a(27) =36199678110a(28) =131086662067a(29) =483853193560