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A276893
Number of ordered set partitions of [n] such that for each block b the smallest integer interval containing b has at most three elements.
3
1, 1, 3, 13, 62, 352, 2348, 17880, 153138, 1458726, 15303672, 175387056, 2180632824, 29240091480, 420683340840, 6464876260440, 105699125013120, 1832140771795440, 33562515077608320, 647929998101403360, 13148236101412979280, 279809650659550924080
OFFSET
0,3
LINKS
FORMULA
a(n) ~ exp(2) * n!. - Vaclav Kotesovec, Sep 22 2016
MATHEMATICA
b[n_, m_, l_List] := b[n, m, l] = If[n == 0, m!, Sum[b[n - 1, Max[m, j], Append[ReplacePart[l, 1 -> Nothing], If[j <= m, 0, j]]], {j, Append[l, m + 1] ~Complement~ {0}}]]; a[n_] := b[n, 0, {0, 0}]; Table[a[n], {n, 0, 21}] (* Jean-François Alcover, Jul 18 2017, after Alois P. Heinz *)
CROSSREFS
Column k=3 of A276890.
Cf. A129847.
Sequence in context: A186242 A367060 A350478 * A284160 A092467 A034478
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 21 2016
STATUS
approved