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a(n) = [ a(n-1)/a(1) + a(n-1)/a(2) + ... + a(n-1)/a(n-1) ] for n >= 3.
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%I #8 Aug 22 2020 15:13:54

%S 1,2,3,5,10,21,45,99,219,485,1076,2389,5306,11786,26182,58164,129215,

%T 287062,637734,1416785,3147520,6992512,15534524,34511410,76670354,

%U 170330428,378405125,840662707,1867611566,4149075406

%N a(n) = [ a(n-1)/a(1) + a(n-1)/a(2) + ... + a(n-1)/a(n-1) ] for n >= 3.

%H Harvey P. Dale, <a href="/A022861/b022861.txt">Table of n, a(n) for n = 1..500</a>

%t nxt[{t_,a_}]:=Module[{c=Floor[Total[a/t]]},{Join[t,{c}],c}]; Join[ {1,2},NestList[ nxt,{{1,2,3},3},30][[All,2]]] (* _Harvey P. Dale_, Aug 22 2020 *)

%K nonn

%O 1,2

%A _Clark Kimberling_