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.

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

Alois P. Heinz, Table of n, a(n) for n = 0..449

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

Adjacent sequences: A276890 A276891 A276892 * A276894 A276895 A276896

Keyword

nonn

Author

Alois P. Heinz, Sep 21 2016

Status

approved