A322884 Number of set partitions of [2n] such that the maximal absolute difference between the least elements of consecutive blocks equals n.

1, 1, 5, 39, 493, 9320, 242366, 8193031, 346270455, 17780116911, 1085004090887, 77324278953174, 6344818280326312, 592415284729545433, 62319734032202722887, 7323734663214254662683, 954467851066831095051393, 137065739258353347820981920

Offset

0,3

Comments

a(0) = 1 by convention.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..130

Wikipedia, Partition of a set

Formula

a(n) = A287215(2n,n).

Example

a(1) = 1: 1|2.
a(2) = 5: 124|3, 12|34, 12|3|4, 13|2|4, 1|23|4.

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-> A(2*n, n)-`if`(n=0, 0, A(2*n, n-1)):
seq(a(n), n=0..20);

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_] := A[2 n, n] - If[n == 0, 0, A[2 n, n - 1]];
Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Jan 03 2019, translated from Maple *)

Crossrefs

Cf. A287215.

Sequence in context: A187739 A067083 A199244 * A352658 A221412 A193118

Adjacent sequences: A322881 A322882 A322883 * A322885 A322886 A322887

Keyword

nonn

Author

Alois P. Heinz, Dec 29 2018

Status

approved