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A322884 Number of set partitions of [2n] such that the maximal absolute difference between the least elements of consecutive blocks equals n. 2
1, 1, 5, 39, 493, 9320, 242366, 8193031, 346270455, 17780116911, 1085004090887, 77324278953174, 6344818280326312, 592415284729545433, 62319734032202722887, 7323734663214254662683, 954467851066831095051393, 137065739258353347820981920 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Jan 03 2019, translated from Maple *)

CROSSREFS

Cf. A287215.

Sequence in context: A122486 A187739 A199244 * A221412 A193118 A227636

Adjacent sequences:  A322881 A322882 A322883 * A322885 A322886 A322887

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Dec 29 2018

STATUS

approved

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Last modified April 23 18:15 EDT 2019. Contains 322387 sequences. (Running on oeis4.)