A350649 Number of partitions of [n] avoiding blocks containing their own index when blocks are ordered with decreasing largest elements.

1, 0, 1, 1, 6, 16, 73, 298, 1453, 7366, 40689, 238258, 1483306, 9746839, 67415262, 489048716, 3710659737, 29372630485, 242021348787, 2071598497189, 18386889241210, 168944811545046, 1604584556714162, 15731291424746912, 159001720653174800, 1654891767547439393

Offset: 0

Author

Alois P. Heinz, Jan 09 2022

Keywords

• nonn

Examples

			a(4) = 6: 432|1, 42|31, 42|3|1, 4|31|2, 4|3|21, 4|3|2|1.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..576
• Wikipedia, Partition of a set

Crossrefs

Column k=0 of A350647, A350684.

Programs

Maple

b:= proc(n, m) option remember; `if`(n=0, 1, add(
      `if`(j=n, 0, b(n-1, max(m, j))), j=1..m+1))
    end:
a:= n-> b(n, 0):
seq(a(n), n=0..25);

Mathematica

b[n_, m_] := b[n, m] = If[n == 0, 1, Sum[
     If[j == n, 0, b[n-1, Max[m, j]]], {j, 1, m+1}]];
a[n_] := b[n, 0];
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, May 16 2022, after Alois P. Heinz *)