A285370 Sum of the entries in the eighth blocks of all set partitions of [n].

8, 333, 7995, 145814, 2250020, 31075944, 397434249, 4813480830, 56089581910, 636257739216, 7090058863984, 78176548855068, 858005254659222, 9419825826737075, 103885234357070729, 1154951013922367450, 12982852258320087936, 147928345019800310188

Offset: 8

Author

Alois P. Heinz, Apr 17 2017

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 8..400
• Wikipedia, Partition of a set

Crossrefs

Column k=8 of A285362.

Programs

Maple

a:= proc(h) option remember; local b; b:=
      proc(n, m) option remember;
        `if`(n=0, [1, 0], add((p-> `if`(j=8, p+ [0,
        (h-n+1)*p[1]], p))(b(n-1, max(m, j))), j=1..m+1))
      end: b(h, 0)[2]
    end:
seq(a(n), n=8..30);

Mathematica

a[h_] := a[h] = Module[{b}, b[n_, m_] := b[n, m] = If[n == 0, {1, 0}, Sum[Function[p, If[j == 8, p + {0, (h - n + 1)*p[[1]]}, p]][b[n - 1, Max[m, j]]], {j, 1, m + 1}]]; b[h, 0][[2]]];
Table[a[n], {n, 8, 30}] (* Jean-François Alcover, May 27 2018, from Maple *)

Formula

a(n) = A285362(n,8).