A287669 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-6 is member of a block >= b-1.

1, 1, 2, 5, 15, 52, 203, 877, 4140, 21146, 115903, 677026, 4190648, 27356008, 187573260, 1346289439, 10084570537, 78630320221, 636692795555, 5342949225111, 46381106554291, 415803352327861, 3843867571153341, 36592205230965683, 358266592635074429

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..45

Wikipedia, Partition of a set

Formula

a(n) = A287641(n,6).

a(n) = A000110(n) for n <= 8.

Example

a(9) = 21146 = 21147 - 1 = A000110(9) - 1 counts all set partitions of [9] except: 1345678|2|9.

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$6]):
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, 6]];
Table[a[n], {n, 0, 20}] (* Jean-François Alcover, May 27 2018, from Maple *)

Crossrefs

Column k=6 of A287641.

Cf. A000110.

Sequence in context: A287586 A287279 A287257 * A099263 A366775 A192865

Adjacent sequences: A287666 A287667 A287668 * A287670 A287671 A287672

Keyword

nonn

Author

Alois P. Heinz, May 29 2017

Status

approved