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A350649
Number of partitions of [n] avoiding blocks containing their own index when blocks are ordered with decreasing largest elements.
3
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
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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jan 09 2022
STATUS
approved