A320559 Number of set partitions of [n] such that for each block b the smallest integer interval containing b has at most nine elements and for at least one block c the smallest integer interval containing c has exactly nine elements.

4140, 30751, 158766, 705926, 2928164, 11774145, 46852653, 186723275, 759062433, 3170429794, 13343960839, 56013146481, 233387096649, 963938933894, 3948441860748, 16062919807404, 65036845178255, 262641546675463, 1059920408695467, 4277149345637299

Offset

9,1

Links

Alois P. Heinz, Table of n, a(n) for n = 9..512

Formula

a(n) = A276725(n) - A276724(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)))(9):
seq(a(n), n=9..40);

Crossrefs

Column k=9 of A276727.

Cf. A276724, A276725, A320622.

Sequence in context: A346861 A251650 A270772 * A294058 A255948 A273658

Adjacent sequences: A320556 A320557 A320558 * A320560 A320561 A320562

Keyword

nonn

Author

Alois P. Heinz, Oct 15 2018

Status

approved