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Floor-sqrt transform of Lah partition numbers (A000262).
1

%I #11 Feb 26 2019 23:06:25

%S 1,1,1,3,8,22,63,193,627,2143,7677,28706,111669,450529,1880164,

%T 8097765,35922614,163849371,767224522,3682984346,18102428784,

%U 91000840873,467393250911,2450438244585,13102651355735,71398380128514,396202573696587

%N Floor-sqrt transform of Lah partition numbers (A000262).

%F a(n) = floor(sqrt(A000262(n))).

%p A000262 := proc(n) option remember: if n=0 then RETURN(1) fi: if n=1 then RETURN(1) fi: (2*n-1)*procname(n-1) - (n-1)*(n-2)*procname(n-2) end proc:

%p A192681 := proc(n) floor(sqrt(A000262(n))) ; end proc: # _R. J. Mathar_, Jul 13 2011

%t FSFromExpSeries[f_,x_,n_] := Map[Floor[Sqrt[#]]&,CoefficientList[Series[f,{x,0,n}],x]Table[k!,{k,0,n}]]

%t FSFromExpSeries[Exp[x/(1-x)],x,60]

%K nonn

%O 0,4

%A _Emanuele Munarini_, Jul 07 2011

%E All terms replaced by _R. J. Mathar_, Jul 13 2011