Self-generating triangle based on symmetric functions.

Terms

a(0) =2a(1) =1a(2) =2a(3) =1a(4) =3a(5) =2a(6) =1a(7) =6a(8) =11a(9) =6a(10) =1a(11) =24a(12) =191a(13) =564a(14) =396a(15) =1a(16) =1176a(17) =435503a(18) =52853928a(19) =1076228496a(20) =1023808896a(21) =1a(22) =2153328000