A285367 Sum of the entries in the fifth blocks of all set partitions of [n].

5, 96, 1148, 11122, 96454, 787959, 6250696, 49115820, 387561065, 3100950735, 25330467332, 212222629466, 1828990798243, 16241051507536, 148696716804278, 1403754413149792, 13658941220426754, 136899626339091133, 1412247058871264298, 14982353645545370808

Offset: 5

Author

Alois P. Heinz, Apr 17 2017

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 5..400
• Wikipedia, Partition of a set

Crossrefs

Column k=5 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=5, 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=5..30);

Mathematica

a[h_] := a[h] = Module[{b}, b[n_, m_] := b[n, m] = If[n == 0, {1, 0}, Sum[Function[p, If[j == 5, 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, 5, 30}] (* Jean-François Alcover, May 27 2018, from Maple *)

Formula

a(n) = A285362(n,5).