a(n) = floor(sqrt(Bell(n))).

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =3a(5) =7a(6) =14a(7) =29a(8) =64a(9) =145a(10) =340a(11) =823a(12) =2052a(13) =5257a(14) =13816a(15) =37188a(16) =102372a(17) =287862a(18) =825879a(19) =2415107a(20) =7191950a(21) =21791507a(22) =67132076a(23) =210123786a(24) =667801519a(25) =2153738687a(26) =7044944749a(27) =23360587491a(28) =78489103731