Number of connected functions on n points with a loop of length 2.

Terms

a(0) =0a(1) =1a(2) =1a(3) =3a(4) =6a(5) =16a(6) =37a(7) =96a(8) =239a(9) =622a(10) =1607a(11) =4235a(12) =11185a(13) =29862a(14) =80070a(15) =216176a(16) =586218a(17) =1597578a(18) =4370721a(19) =12003882a(20) =33077327a(21) =91433267a(22) =253454781a(23) =704429853a(24) =1962537755a(25) =5479855546a(26) =15332668869a(27) =42983656210a(28) =120716987723a(29) =339596063606