A276895 Number of ordered set partitions of [n] such that for each block b the smallest integer interval containing b has at most five elements.

1, 1, 3, 13, 75, 541, 4142, 34792, 322904, 3303160, 37046948, 451109712, 5923255272, 83424945768, 1254842021634, 20081656282038, 340747127912616, 6111343349250912, 115529870445001392, 2296160998268520576, 47869541875153872144, 1044601509263870430000

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=5 of A276890.

Cf. A276721.

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

Formula

a(n) ~ exp(4) * n!. - Vaclav Kotesovec, Sep 22 2016