A285368 Sum of the entries in the sixth blocks of all set partitions of [n].

6, 154, 2380, 28975, 308127, 3018824, 28133574, 254715640, 2274064881, 20242054046, 181155397430, 1640541610028, 15107388580258, 141982420633882, 1365335004650614, 13456694682282849, 136069364339492065, 1412201447170038064, 15044059353340996950

Offset

6,1

Links

Alois P. Heinz, Table of n, a(n) for n = 6..400

Wikipedia, Partition of a set

Formula

a(n) = A285362(n,6).

Maple

a:= proc(h) option remember; local b; b:=
      proc(n, m) option remember;
        `if`(n=0, [1, 0], add((p-> `if`(j=6, 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=6..30);

Mathematica

a[h_] := a[h] = Module[{b}, b[n_, m_] := b[n, m] = If[n == 0, {1, 0}, Sum[Function[p, If[j == 6, 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, 6, 30}] (* Jean-François Alcover, May 27 2018, from Maple *)

Crossrefs

Column k=6 of A285362.

Sequence in context: A185211 A046182 A092122 * A003460 A157626 A229098

Adjacent sequences: A285365 A285366 A285367 * A285369 A285370 A285371

Keyword

nonn

Author

Alois P. Heinz, Apr 17 2017

Status

approved