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a(n) = sum((-1)^(n-k)*floor(sqrt(Bell(k))),k=0..n).
3

%I #6 Mar 30 2012 18:55:30

%S 1,0,1,1,2,5,9,20,44,101,239,584,1468,3789,10027,27161,75211,212651,

%T 613228,1801879,5390071,16401436,50730640,159393146,508408373,

%U 1645330314,5399614435,17960973056,60528130675

%N a(n) = sum((-1)^(n-k)*floor(sqrt(Bell(k))),k=0..n).

%t Table[Sum[(-1)^(n-k)Floor[Sqrt[BellB[k]]],{k,0,n}],{n,0,100}]

%o (Maxima) makelist(sum((-1)^(n-k)*floor(sqrt(belln(k))),k,0,n),n,0,28);

%Y Cf. A000110, A192570, A192571.

%K nonn

%O 0,5

%A _Emanuele Munarini_, Jul 04 2011