Self-generating triangle based on symmetric functions.

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =2a(5) =1a(6) =1a(7) =4a(8) =5a(9) =2a(10) =1a(11) =12a(12) =49a(13) =78a(14) =40a(15) =1a(16) =180a(17) =11085a(18) =270610a(19) =2094264a(20) =1834560a(21) =1a(22) =4210700