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

0,3

Links

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

Formula

a(n) ~ exp(4) * 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, {0, 0, 0, 0}]; Table[a[n], {n, 0, 21}] (* Jean-François Alcover, Jul 18 2017, after Alois P. Heinz *)

Crossrefs

Column k=5 of A276890.

Cf. A276721.

Sequence in context: A173990 A276924 A343788 * A276925 A343789 A276896

Adjacent sequences: A276892 A276893 A276894 * A276896 A276897 A276898

Keyword

nonn

Author

Alois P. Heinz, Sep 21 2016

Status

approved