A276894 Number of ordered set partitions of [n] such that for each block b the smallest integer interval containing b has at most four elements.

1, 1, 3, 13, 75, 466, 3272, 26032, 232820, 2304600, 25003176, 295139034, 3767545662, 51729553992, 760326663792, 11913105530016, 198246166468224, 3492246172917240, 64928731038925800, 1270685662509505560, 26112819120798942120, 562241528313838756560

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=4 of A276890.

Cf. A276720.

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, 0}]; Table[a[n], {n, 0, 21}] (* Jean-François Alcover, Jul 18 2017, after Alois P. Heinz *)

Formula

a(n) ~ exp(3) * n!. - Vaclav Kotesovec, Sep 22 2016