A285365 Sum of the entries in the third blocks of all set partitions of [n].

3, 28, 185, 1094, 6293, 36619, 219931, 1376929, 9023266, 61944014, 445076570, 3341575188, 26164558199, 213243368898, 1805626838935, 15856747810014, 144189514375955, 1355629263039685, 13159535002316403, 131729480987412527, 1358188539892586220

Offset

3,1

Links

Alois P. Heinz, Table of n, a(n) for n = 3..400

Wikipedia, Partition of a set

Formula

a(n) = A285362(n,3).

Example

a(3) = 3 because the sum of the entries in the third blocks of all set partitions of [3] (123, 12|3, 13|2, 1|23, 1|2|3) is 0+0+0+0+3 = 3.

Maple

a:= proc(h) option remember; local b; b:=
      proc(n, m) option remember;
        `if`(n=0, [1, 0], add((p-> `if`(j=3, 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=3..30);

Mathematica

a[h_] := a[h] = Module[{b}, b[n_, m_] := b[n, m] = If[n == 0, {1, 0}, Sum[Function[p, If[j == 3, 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, 3, 30}] (* Jean-François Alcover, May 27 2018, from Maple *)

Crossrefs

Column k=3 of A285362.

Sequence in context: A302522 A303405 A074922 * A366689 A160872 A081019

Adjacent sequences: A285362 A285363 A285364 * A285366 A285367 A285368

Keyword

nonn

Author

Alois P. Heinz, Apr 17 2017

Status

approved