A320560 Number of set partitions of [n] such that for each block b the smallest integer interval containing b has at most ten elements and for at least one block c the smallest integer interval containing c has exactly ten elements.

21147, 172649, 977607, 4732307, 21196160, 91356135, 387221998, 1635077589, 6933701115, 29953216031, 132647186513, 592562183163, 2645622362009, 11748752847703, 51794376799161, 226629372792025, 984996790932516, 4257860514411454, 18336632254191876

Offset: 10

Author

Alois P. Heinz, Oct 15 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 10..512

Crossrefs

Column k=10 of A276727.

Cf. A276725, A276726, A320623.

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)))(10):
seq(a(n), n=10..40);

Formula

a(n) = A276726(n) - A276725(n).