A285364 Sum of the entries in the second blocks of all set partitions of [n].

2, 12, 58, 273, 1329, 6839, 37423, 217606, 1340597, 8719806, 59680387, 428481322, 3218109788, 25220647760, 205790862332, 1744755841379, 15342274425585, 139692065365753, 1314995731359189, 12780466391685166, 128081591768679823, 1322011886920066940

Offset: 2

Author

Alois P. Heinz, Apr 17 2017

Keywords

• nonn

Examples

			a(3) = 12 because the sum of the entries in the second blocks of all set partitions of [3] (123, 12|3, 13|2, 1|23, 1|2|3) is 0+3+2+5+2 = 12.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 2..575
• Wikipedia, Partition of a set

Crossrefs

Column k=2 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=2, 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=2..30);

Mathematica

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

Formula

a(n) = A285362(n,2).