A322880 Number of set partitions of [n] such that the maximal absolute difference between the least elements of consecutive blocks equals seven.

0, 1, 67, 1059, 11373, 106256, 940608, 8193031, 71568443, 633413486, 5710573774, 52579554510, 494986212033, 4766754646529, 46966622143740, 473477764449909, 4883216510830794, 51513192445470426, 555667122424414886, 6127026713823497897, 69034256792655555566

Offset: 7

Author

Alois P. Heinz, Dec 29 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 7..580
• Wikipedia, Partition of a set

Crossrefs

Column k=7 of A287215.

Cf. A287256, A287257.

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))(7):
seq(a(n), n=7..30);

Formula

a(n) = A287257(n) - A287256(n).