A270762 Total sum of the sizes of all blocks with maximal element 8 in all set partitions of {1,2,...,n}.

10279, 39848, 174029, 838485, 4395802, 24825947, 149888167, 961547874, 6521484087, 46567171489, 348842020704, 2733150610201, 22336983535651, 189972322541416, 1677852685522313, 15360428047484945, 145515022547392842, 1424312554941600127, 14384441797357797779

Offset: 8

Author

Alois P. Heinz, Mar 22 2016

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 8..577
• Wikipedia, Partition of a set

Crossrefs

Column k=8 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 - 8]][[2]];
Array[a, 24, 8] (* Jean-François Alcover, May 26 2018, from Maple code for A270701 *)