A320556 Number of set partitions of [n] such that for each block b the smallest integer interval containing b has at most six elements and for at least one block c the smallest integer interval containing c has exactly six elements.

52, 265, 966, 3172, 10100, 32918, 111138, 373888, 1238236, 4034221, 12991481, 41567855, 132719006, 423099220, 1346053178, 4271656023, 13520858094, 42696919677, 134582517515, 423599583268, 1331701708711, 4182193622677, 13121508724973, 41131777789545

Offset

6,1

Links

Alois P. Heinz, Table of n, a(n) for n = 6..1000

Formula

a(n) = A276722(n) - A276721(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)))(6):
seq(a(n), n=6..50);

Crossrefs

Column k=6 of A276727.

Cf. A276721, A276722, A320619.

Sequence in context: A086860 A070147 A236517 * A252335 A230533 A235654

Adjacent sequences: A320553 A320554 A320555 * A320557 A320558 A320559

Keyword

nonn,easy

Author

Alois P. Heinz, Oct 15 2018

Status

approved