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

10,1

Links

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

Formula

a(n) = A276726(n) - A276725(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)))(10):
seq(a(n), n=10..40);

Crossrefs

Column k=10 of A276727.

Cf. A276725, A276726, A320623.

Sequence in context: A346829 A346862 A270773 * A294059 A255949 A273659

Adjacent sequences: A320557 A320558 A320559 * A320561 A320562 A320563

Keyword

nonn

Author

Alois P. Heinz, Oct 15 2018

Status

approved