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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
OFFSET
0,3
COMMENTS
a(0) = 1 by convention.
LINKS
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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Dec 29 2018
STATUS
approved