A285410 Sum of the entries in the (n+1)-th blocks of all set partitions of [2n+1].

1, 12, 185, 3757, 96454, 3018824, 111964040, 4813480830, 235727269842, 12967143328027, 792113203502422, 53224214308284463, 3902445739220008603, 310108348556403600064, 26551900616231571763742, 2437107937223749442138164, 238735439946016510599661488

Offset: 0

Author

Alois P. Heinz, Apr 18 2017

Keywords

• nonn

Examples

			a(1) = 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 = 0..345
• Wikipedia, Partition of a set

Crossrefs

Cf. A270529, 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=h+1, p+ [0,
        (2*h-n+2)*p[1]], p))(b(n-1, max(m, j))), j=1..m+1))
      end: b(2*h+1, 0)[2]
    end:
seq(a(n), n=0..20);

Mathematica

a[h_] := a[h] = Module[{b}, b[0, ] = {1, 0}; b[n, m_] := b[n, m] = Sum[ If[j == h + 1, # + {0, (2*h - n + 2)*#[[1]]}, #]&[b[n - 1, Max[m, j]]], {j, 1, m + 1}]; b[2*h + 1, 0][[2]]];
Table[a[n], {n, 0, 20}] (* Jean-François Alcover, May 23 2018, translated from Maple *)

Formula

a(n) = A285362(2n+1,n+1).