A287668 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-5 is member of a block >= b-1.

1, 1, 2, 5, 15, 52, 203, 877, 4139, 21107, 115301, 670059, 4119316, 26665103, 181031235, 1284643851, 9500643629, 73037739470, 582346938182, 4805997066022, 40980051074202, 360452146946076, 3265691382361850, 30435437254066599, 291431082211368120

Offset: 0

Author

Alois P. Heinz, May 29 2017

Keywords

• nonn

Examples

			a(8) = 4139 = 4140 - 1 = A000110(8) - 1 counts all set partitions of [8] except: 134567|2|8.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..55

Crossrefs

Column k=5 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$5]):
seq(a(n), n=0..24);

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, {5}]];
a /@ Range[0, 24] (* Jean-François Alcover, Dec 11 2020, after Alois P. Heinz *)

Formula

a(n) = A287641(n,5).

a(n) = A000110(n) for n <= 7.