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

Author

Alois P. Heinz, Oct 15 2018

Keywords

• nonn

Links

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

Crossrefs

Column k=9 of A276727.

Cf. A276724, A276725, A320622.

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

Formula

a(n) = A276725(n) - A276724(n).