A322882 Number of set partitions of [n] such that the maximal absolute difference between the least elements of consecutive blocks equals nine.

0, 1, 259, 7851, 123693, 1517480, 16628928, 172861375, 1757583339, 17780116911, 180778826049, 1858914009077, 19407229306905, 206203531592425, 2232778235440364, 24655217395787251, 277719538910592762, 3191229583066629810, 37404691679158439649

Offset

9,3

Links

Alois P. Heinz, Table of n, a(n) for n = 9..579

Wikipedia, Partition of a set

Formula

a(n) = A287259(n) - A287258(n).

Maple

b:= proc(n, k, m, l) option remember; `if`(n<1, 1,
     `if`(l-n>k, 0, b(n-1, k, m+1, n))+m*b(n-1, k, m, l))
    end:
A:= (n, k)-> b(n-1, min(k, n-1), 1, n):
a:= n-> (k-> A(n, k)-A(n, k-1))(9):
seq(a(n), n=9..30);

Crossrefs

Column k=9 of A287215.

Cf. A287258, A287259.

Sequence in context: A309763 A344193 A254642 * A256594 A229433 A022221

Adjacent sequences: A322879 A322880 A322881 * A322883 A322884 A322885

Keyword

nonn

Author

Alois P. Heinz, Dec 29 2018

Status

approved