A270756 Total sum of the sizes of all blocks with maximal element 2 in all set partitions of {1,2,...,n}.

3, 4, 9, 25, 82, 307, 1283, 5894, 29427, 158269, 910520, 5570737, 36071631, 246188196, 1764757189, 13246059237, 103825154098, 847806545767, 7196895817375, 63389642645486, 578318132627495, 5456455370760825, 53165437331978992, 534262881004973981

Offset: 2

Author

Alois P. Heinz, Mar 22 2016

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 2..577
• Wikipedia, Partition of a set

Crossrefs

Column k=2 of A270701.

A diagonal of A270702.

Programs

Mathematica

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}]];
a[n_] := b[n, 0, Max[0, 1 + n - 2]][[2]];
Array[a, 24, 2] (* Jean-François Alcover, May 26 2018, from Maple code for A270701 *)