a(n) = binomial(n, A002024(n+1)-1) where A002024 is "n appears n times".

Terms

a(0) =1a(1) =1a(2) =2a(3) =3a(4) =6a(5) =10a(6) =20a(7) =35a(8) =56a(9) =84a(10) =210a(11) =330a(12) =495a(13) =715a(14) =1001a(15) =3003a(16) =4368a(17) =6188a(18) =8568a(19) =11628a(20) =15504a(21) =54264a(22) =74613a(23) =100947a(24) =134596a(25) =177100a(26) =230230a(27) =296010a(28) =1184040a(29) =1560780