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

Terms

a(0) =1a(1) =1a(2) =1a(3) =3a(4) =5a(5) =11a(6) =27a(7) =61a(8) =151a(9) =375a(10) =1001a(11) =2699a(12) =7635a(13) =22069a(14) =65695a(15) =199671a(16) =620417a(17) =1966715a(18) =6367323a(19) =21059149a(20) =71216311a(21) =246322503a(22) =871268465a(23) =3148964147a(24) =11613253707a(25) =43625643373a(26) =166606282471a(27) =645633978279