a(n) = 2*A040027(n-1) + Bell(n), where Bell = A000110.

Terms

a(0) =1a(1) =3a(2) =4a(3) =11a(4) =33a(5) =114a(6) =445a(7) =1923a(8) =9078a(9) =46369a(10) =254297a(11) =1487896a(12) =9239135a(13) =60615819a(14) =418583924a(15) =3032405831a(16) =22979752405a(17) =181697363626