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

0,3

Links

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

Formula

a(n) ~ exp(3) * 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}]; Table[a[n], {n, 0, 21}] (* Jean-François Alcover, Jul 18 2017, after Alois P. Heinz *)

Crossrefs

Column k=4 of A276890.

Cf. A276720.

Sequence in context: A009382 A110193 A038762 * A074517 A251658 A330047

Adjacent sequences: A276891 A276892 A276893 * A276895 A276896 A276897

Keyword

nonn

Author

Alois P. Heinz, Sep 21 2016

Status

approved