A287671 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-8 is member of a block >= b-1.

1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115975, 678569, 4213333, 27634757, 190697165, 1379679500, 10433619205, 82253035850, 674373619108, 5738060816421, 50573749394877, 460936356129618, 4337525923676113, 42084057817903853, 420444371318055912

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..33

Wikipedia, Partition of a set

Formula

a(n) = A287641(n,8).

a(n) = A000110(n) for n <= 10.

Example

a(11) = 678569 = 678570 - 1 = A000110(11) - 1 counts all set partitions of [11] except: 13456789(10)|2|(11).

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$8]):
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, 8]];
Table[a[n], {n, 0, 20}] (* Jean-François Alcover, May 27 2018, from Maple *)

Crossrefs

Column k=8 of A287641.

Cf. A000110.

Sequence in context: A287588 A287281 A287259 * A164864 A366776 A192866

Adjacent sequences: A287668 A287669 A287670 * A287672 A287673 A287674

Keyword

nonn

Author

Alois P. Heinz, May 29 2017

Status

approved