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

7,3

Links

Alois P. Heinz, Table of n, a(n) for n = 7..580

Wikipedia, Partition of a set

Formula

a(n) = A287257(n) - A287256(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))(7):
seq(a(n), n=7..30);

Crossrefs

Column k=7 of A287215.

Cf. A287256, A287257.

Sequence in context: A254640 A093267 A032651 * A157665 A231193 A078850

Adjacent sequences: A322877 A322878 A322879 * A322881 A322882 A322883

Keyword

nonn

Author

Alois P. Heinz, Dec 29 2018

Status

approved