A287670 Number of set partitions of [n] such that j is member of block b only if b = 1 or at least one of j-1, ..., j-7 is member of a block >= b-1.

1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115974, 678434, 4209827, 27578206, 189954361, 1370870811, 10334533723, 81166980407, 662588540048, 5610196619724, 49177794178940, 445536788068643, 4165402700226511, 40131393651398259, 397935154986242021

Offset: 0

Author

Alois P. Heinz, May 29 2017

Keywords

• nonn

Examples

			a(10) = 115974 = 115975 - 1 = A000110(10) - 1 counts all set partitions of [10] except: 13456789|2|(10).
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..37
• Wikipedia, Partition of a set

Crossrefs

Column k=7 of A287641.

Cf. A000110.

Programs

Maple

b:= proc(n, l) option remember; `if`(n=0, 1, add(b(n-1,
      [seq(max(l[i], j), i=2..nops(l)), j]), j=1..l[1]+1))
    end:
a:= n-> b(n, [0$7]):
seq(a(n), n=0..20);

Mathematica

b[n_, l_] := b[n, l] = If[n == 0, 1, Sum[b[n - 1, Append[Table[Max[l[[i]], j], {i, 2, Length[l]}], j]], {j, 1, l[[1]] + 1}]];
a[n_] := b[n, Table[0, 7]];
Table[a[n], {n, 0, 20}] (* Jean-François Alcover, May 27 2018, from Maple *)

Formula

a(n) = A287641(n,7).

a(n) = A000110(n) for n <= 9.