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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.
3
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
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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 21 2016
STATUS
approved