From the enumeration of involutions avoiding the pattern 4321.

Terms

a(0) =0a(1) =0a(2) =0a(3) =0a(4) =0a(5) =2a(6) =6a(7) =18a(8) =47a(9) =123a(10) =318a(11) =830a(12) =2182a(13) =5792a(14) =15504a(15) =41828a(16) =113626a(17) =310564a(18) =853458a(19) =2356770a(20) =6536372a(21) =18199274a(22) =50852008a(23) =142547548a(24) =400763211a(25) =1129760403a(26) =3192727784a(27) =9043402488a(28) =25669818462a(29) =73007772788