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

0,5

Links

Alois P. Heinz, Table of n, a(n) for n = 0..576

Wikipedia, Partition of a set

Example

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

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 *)

Crossrefs

Column k=0 of A350647, A350684.

Sequence in context: A277747 A142704 A083885 * A211954 A230942 A188570

Adjacent sequences: A350646 A350647 A350648 * A350650 A350651 A350652

Keyword

nonn

Author

Alois P. Heinz, Jan 09 2022

Status

approved