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A270757 Total sum of the sizes of all blocks with maximal element 3 in all set partitions of {1,2,...,n}.

%I A270757 #8 May 26 2018 11:20:35
%S A270757 9,16,41,127,456,1845,8257,40338,212983,1205911,7275802,46534535,
%T A270757 314117861,2229489144,16584674293,128934314027,1044976711816,
%U A270757 8809644039105,77101357474077,699264675713410,6561367477780443,63603478257343891,636087039930484642
%N A270757 Total sum of the sizes of all blocks with maximal element 3 in all set partitions of {1,2,...,n}.
%H A270757 Alois P. Heinz, <a href="/A270757/b270757.txt">Table of n, a(n) for n = 3..577</a>
%H A270757 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%t A270757 b[n_, m_, t_] := b[n, m, t] = If[n == 0, {1, 0}, Sum[If[t == 1 && j != m + 1, 0, Function[p, p + If[j == -t || t == 1 && j == m + 1, {0, p[[1]]}, 0]][b[n - 1, Max[m, j], If[t == 1 && j == m + 1, -j, If[t < 0, t, If[t > 0, t - 1, 0]]]]]], {j, 1, m + 1}]];
%t A270757 a[n_] := b[n, 0, Max[0, 1 + n - 3]][[2]];
%t A270757 Array[a, 24, 3] (* _Jean-François Alcover_, May 26 2018, from Maple code for A270701 *)
%Y A270757 Column k=3 of A270701.
%Y A270757 A diagonal of A270702.
%K A270757 nonn
%O A270757 3,1
%A A270757 _Alois P. Heinz_, Mar 22 2016