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

9, 16, 41, 127, 456, 1845, 8257, 40338, 212983, 1205911, 7275802, 46534535, 314117861, 2229489144, 16584674293, 128934314027, 1044976711816, 8809644039105, 77101357474077, 699264675713410, 6561367477780443, 63603478257343891, 636087039930484642

Offset: 3

Author

Alois P. Heinz, Mar 22 2016

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 3..577
• Wikipedia, Partition of a set

Crossrefs

Column k=3 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 - 3]][[2]];
Array[a, 24, 3] (* Jean-François Alcover, May 26 2018, from Maple code for A270701 *)