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

Author

Alois P. Heinz, Dec 29 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 8..580
• Wikipedia, Partition of a set

Crossrefs

Column k=8 of A287215.

Cf. A287257, A287258.

Programs

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);

Formula

a(n) = A287258(n) - A287257(n).