A322878 Number of set partitions of [n] such that the maximal absolute difference between the least elements of consecutive blocks equals five.

0, 1, 19, 171, 1293, 9320, 66992, 488526, 3637440, 27735903, 216992278, 1743777862, 14401360577, 122242150172, 1066284279026, 9554869690126, 87923414758506, 830459368379431, 8047463255217118, 79967170844047637, 814439368083686232, 8497321384591725159

Offset

5,3

Links

Alois P. Heinz, Table of n, a(n) for n = 5..582

Wikipedia, Partition of a set

Formula

a(n) = A287255(n) - A287254(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))(5):
seq(a(n), n=5..30);

Mathematica

b[n_, k_, m_, l_] := b[n, k, m, l] = If[n < 1, 1, If[l - n > k, 0, b[n - 1, k, m + 1, n]] + m b[n - 1, k, m, l]];
A[n_, k_] := b[n - 1, Min[k, n - 1], 1, n];
a[n_] := With[{k = 5}, A[n, k] - A[n, k - 1]];
a /@ Range[5, 30] (* Jean-François Alcover, May 05 2020, after Maple *)

Crossrefs

Column k=5 of A287215.

Cf. A287254, A287255.

Sequence in context: A010935 A282288 A022614 * A060222 A041690 A217698

Adjacent sequences: A322875 A322876 A322877 * A322879 A322880 A322881

Keyword

nonn

Author

Alois P. Heinz, Dec 29 2018

Status

approved