a(n) = sum(floor(sqrt(Bell(k))),k=0..n).

Terms

a(0) =1a(1) =2a(2) =3a(3) =5a(4) =8a(5) =15a(6) =29a(7) =58a(8) =122a(9) =267a(10) =607a(11) =1430a(12) =3482a(13) =8739a(14) =22555a(15) =59743a(16) =162115a(17) =449977a(18) =1275856a(19) =3690963a(20) =10882913a(21) =32674420a(22) =99806496a(23) =309930282a(24) =977731801a(25) =3131470488a(26) =10176415237a(27) =33537002728a(28) =112026106459