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Sum of max{S(i,j): 1<=j<=i} for i = 1,2,...,n, where S(i,j) are Stirling numbers of the second kind.
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%I #8 Jan 23 2018 16:42:50

%S 1,2,5,12,37,127,477,2178,9948,52473,299203,1678603,10999915,74436288,

%T 495129561,3777012165,29485116951,226947600351,1936698603831,

%U 17107631266510,149618646613594,1391581950147514,13711650761944414,134334225088016914,1337497617263404414

%N Sum of max{S(i,j): 1<=j<=i} for i = 1,2,...,n, where S(i,j) are Stirling numbers of the second kind.

%H Robert Israel, <a href="/A024717/b024717.txt">Table of n, a(n) for n = 1..576</a>

%p A002870:= [seq(max(seq(combinat:-stirling2(i,j),j=1..i)),i=1..50)]:

%p ListTools:-PartialSums(A002870); # _Robert Israel_, Jan 23 2018

%Y First differences are in A002870.

%K nonn

%O 1,2

%A _Clark Kimberling_