Number of connected functions on n points with a loop of length 3.

Terms

a(0) =1a(1) =1a(2) =3a(3) =9a(4) =23a(5) =62a(6) =169a(7) =451a(8) =1217a(9) =3291a(10) =8916a(11) =24243a(12) =66155a(13) =181053a(14) =497134a(15) =1369064a(16) =3780942a(17) =10469573a(18) =29063361a(19) =80867990a(20) =225508124a(21) =630145449a(22) =1764240907a(23) =4948365051a(24) =13902893423a(25) =39124094362a(26) =110265280739a(27) =311208414556a(28) =879523722747