Shifts 2 places left when e.g.f. is squared.

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =4a(5) =10a(6) =30a(7) =100a(8) =380a(9) =1600a(10) =7400a(11) =37400a(12) =204600a(13) =1205600a(14) =7612000a(15) =51260000a(16) =366784000a(17) =2778820000a(18) =22222332000a(19) =187067320000