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A322875
Number of set partitions of [n] such that the maximal absolute difference between the least elements of consecutive blocks equals two.
2
0, 1, 5, 21, 86, 361, 1584, 7315, 35635, 183080, 990659, 5635021, 33622161, 209973099, 1369560267, 9310957518, 65852852210, 483672626464, 3683088047043, 29033382412670, 236591717703447, 1990467019391404, 17268021545339042, 154304401318961489
OFFSET
2,3
LINKS
FORMULA
a(n) = A287252(n) - A026898(n-1).
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))(2):
seq(a(n), n=2..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 = 2}, A[n, k] - A[n, k - 1]];
a /@ Range[2, 30] (* Jean-François Alcover, Dec 14 2020, after Alois P. Heinz *)
CROSSREFS
Column k=2 of A287215.
Sequence in context: A265939 A012814 A039919 * A292494 A010925 A019992
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Dec 29 2018
STATUS
approved