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

0,3

Links

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

Formula

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

Crossrefs

Column k=6 of A276890.

Cf. A276722.

Sequence in context: A276895 A276925 A343789 * A276926 A343790 A276897

Adjacent sequences: A276893 A276894 A276895 * A276897 A276898 A276899

Keyword

nonn

Author

Alois P. Heinz, Sep 21 2016

Status

approved