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%I #10 May 26 2018 11:20:39
%S 3,4,9,25,82,307,1283,5894,29427,158269,910520,5570737,36071631,
%T 246188196,1764757189,13246059237,103825154098,847806545767,
%U 7196895817375,63389642645486,578318132627495,5456455370760825,53165437331978992,534262881004973981
%N Total sum of the sizes of all blocks with maximal element 2 in all set partitions of {1,2,...,n}.
%H Alois P. Heinz, <a href="/A270756/b270756.txt">Table of n, a(n) for n = 2..577</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%t 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 a[n_] := b[n, 0, Max[0, 1 + n - 2]][[2]];
%t Array[a, 24, 2] (* _Jean-François Alcover_, May 26 2018, from Maple code for A270701 *)
%Y Column k=2 of A270701.
%Y A diagonal of A270702.
%K nonn
%O 2,1
%A _Alois P. Heinz_, Mar 22 2016