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

Author

Alois P. Heinz, Dec 29 2018

Keywords

• nonn

Comments

a(0) = 1 by convention.

Examples

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

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..130
• Wikipedia, Partition of a set

Crossrefs

Cf. A287215.

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-> 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 *)

Formula

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