A322881 Number of set partitions of [n] such that the maximal absolute difference between the least elements of consecutive blocks equals eight.

0, 1, 131, 2837, 36733, 392532, 3862958, 36745885, 346270455, 3276723147, 31384368348, 305668217577, 3035028866706, 30761374688048, 318435571825333, 3367380704425616, 36376061350280633, 401367264163810215, 4522617803400779891, 52030240381937090624

Offset

8,3

Links

Alois P. Heinz, Table of n, a(n) for n = 8..580

Wikipedia, Partition of a set

Formula

a(n) = A287258(n) - A287257(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))(8):
seq(a(n), n=8..30);

Crossrefs

Column k=8 of A287215.

Cf. A287257, A287258.

Sequence in context: A144247 A161197 A254641 * A104596 A091743 A066621

Adjacent sequences: A322878 A322879 A322880 * A322882 A322883 A322884

Keyword

nonn

Author

Alois P. Heinz, Dec 29 2018

Status

approved