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a(n) = floor(3rd elementary symmetric function of Sum_{j=1..k} 1/j, k = 1,2,...,n).
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%I #11 Dec 12 2022 18:09:58

%S 2,15,49,122,255,472,804,1284,1950,2842,4005,5488,7341,9619,12380,

%T 15683,19594,24177,29503,35642,42669,50662,59699,69863,81238,93910,

%U 107969,123505,140612,159386,179924,202326,226695,253132,281746,312643,345934,381729

%N a(n) = floor(3rd elementary symmetric function of Sum_{j=1..k} 1/j, k = 1,2,...,n).

%H Robert Israel, <a href="/A025213/b025213.txt">Table of n, a(n) for n = 3..300</a>

%p es3:= proc(L) convert(map(convert,combinat:-choose(L,3),`*`),`+`) end proc:

%p f:= proc(n) local k; floor(es3(ListTools:-PartialSums([seq(1/k,k=1..n)]))) end proc:

%p map(f, [$3..50]); # _Robert Israel_, Dec 12 2022

%K nonn

%O 3,1

%A _Clark Kimberling_