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

Author

Alois P. Heinz, Sep 21 2016

Keywords

• nonn

Links

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

Crossrefs

Column k=3 of A276890.

Cf. A129847.

Programs

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 *)

Formula

a(n) ~ exp(2) * n!. - Vaclav Kotesovec, Sep 22 2016