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