a(n)=Product[p(n)-j, j=1..n]/n!=A090114(n)/n!.

Terms

a(0) =1a(1) =1a(2) =4a(3) =15a(4) =252a(5) =924a(6) =11440a(7) =43758a(8) =497420a(9) =13123110a(10) =54627300a(11) =1251677700a(12) =12033222880a(13) =52860229080a(14) =511738760544