A285369 Sum of the entries in the seventh blocks of all set partitions of [n].

7, 232, 4518, 67898, 875365, 10228471, 111964040, 1173487986, 11959590504, 119889568676, 1192711559418, 11859084564254, 118526150123309, 1196311505171568, 12239696866561282, 127315711586330538, 1349476206629576995, 14599608027440148129, 161399084259928978190

Offset: 7

Author

Alois P. Heinz, Apr 17 2017

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 7..400
• Wikipedia, Partition of a set

Crossrefs

Column k=7 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=7, 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=7..30);

Mathematica

a[h_] := a[h] = Module[{b}, b[n_, m_] := b[n, m] = If[n == 0, {1, 0}, Sum[Function[p, If[j == 7, 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, 7, 30}] (* Jean-François Alcover, May 27 2018, from Maple *)

Formula

a(n) = A285362(n,7).