A320558 Number of set partitions of [n] such that for each block b the smallest integer interval containing b has at most eight elements and for at least one block c the smallest integer interval containing c has exactly eight elements.

877, 5852, 27267, 110545, 422396, 1578192, 5877165, 22355618, 87597223, 345223398, 1352883364, 5249340393, 20158426185, 76729396494, 290259302392, 1094289866107, 4121529511428, 15518374075986, 58402401729381, 219602989556557, 824720185307142, 3092742982300231

Offset

8,1

Links

Alois P. Heinz, Table of n, a(n) for n = 8..1000

Formula

a(n) = A276724(n) - A276723(n).

Maple

b:= proc(n, m, l) option remember; `if`(n=0, 1,
      add(b(n-1, max(m, j), [subsop(1=NULL, l)[],
      `if`(j<=m, 0, j)]), j={l[], m+1} minus {0}))
    end:
A:= (n, k)-> `if`(n=0, 1, `if`(k<2, k, b(n, 0, [0$(k-1)]))):
a:= n-> (k-> A(n, k) -`if`(k=0, 0, A(n, k-1)))(8):
seq(a(n), n=8..50);

Crossrefs

Column k=8 of A276727.

Cf. A276723, A276724, A320621.

Sequence in context: A211566 A346827 A346860 * A270771 A154090 A294057

Adjacent sequences: A320555 A320556 A320557 * A320559 A320560 A320561

Keyword

nonn,easy

Author

Alois P. Heinz, Oct 15 2018

Status

approved