A320557 Number of set partitions of [n] such that for each block b the smallest integer interval containing b has at most seven elements and for at least one block c the smallest integer interval containing c has exactly seven elements.

203, 1197, 4971, 18223, 63768, 220419, 779242, 2845864, 10418560, 37768970, 135153976, 477964329, 1676343822, 5852483376, 20403590238, 71080014610, 247360604490, 859493636214, 2980904955378, 10318666659192, 35656973487023, 123042978647274, 424121272321296

Offset: 7

Author

Alois P. Heinz, Oct 15 2018

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 7..1000

Crossrefs

Column k=7 of A276727.

Cf. A276722, A276723, A320620.

Programs

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)))(7):
seq(a(n), n=7..50);

Formula

a(n) = A276723(n) - A276722(n).