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

7,1

Links

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

Formula

a(n) = A276723(n) - A276722(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)))(7):
seq(a(n), n=7..50);

Crossrefs

Column k=7 of A276727.

Cf. A276722, A276723, A320620.

Sequence in context: A346826 A346859 A272390 * A270770 A294056 A255946

Adjacent sequences: A320554 A320555 A320556 * A320558 A320559 A320560

Keyword

nonn,easy

Author

Alois P. Heinz, Oct 15 2018

Status

approved