A276896 Number of ordered set partitions of [n] such that for each block b the smallest integer interval containing b has at most six elements.

1, 1, 3, 13, 75, 541, 4683, 42610, 417464, 4438936, 51245936, 640642456, 8640223604, 124868055888, 1924066147008, 31484641736040, 545300469146760, 9967163998036554, 191772882094520910, 3874791064947232008, 82035921068376624096, 1816274191193756670912

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=6 of A276890.

Cf. A276722.

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, Table[0, {5}]]; Table[a[n], {n, 0, 21}] (* Jean-François Alcover, Jul 18 2017, after Alois P. Heinz *)

Formula

a(n) ~ exp(5) * n!. - Vaclav Kotesovec, Sep 22 2016