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A287669
Number of set partitions of [n] such that j is member of block b only if b = 1 or at least one of j-1, ..., j-6 is member of a block >= b-1.
2
1, 1, 2, 5, 15, 52, 203, 877, 4140, 21146, 115903, 677026, 4190648, 27356008, 187573260, 1346289439, 10084570537, 78630320221, 636692795555, 5342949225111, 46381106554291, 415803352327861, 3843867571153341, 36592205230965683, 358266592635074429
OFFSET
0,3
LINKS
FORMULA
a(n) = A287641(n,6).
a(n) = A000110(n) for n <= 8.
EXAMPLE
a(9) = 21146 = 21147 - 1 = A000110(9) - 1 counts all set partitions of [9] except: 1345678|2|9.
MAPLE
b:= proc(n, l) option remember; `if`(n=0, 1, add(b(n-1,
[seq(max(l[i], j), i=2..nops(l)), j]), j=1..l[1]+1))
end:
a:= n-> b(n, [0$6]):
seq(a(n), n=0..20);
MATHEMATICA
b[n_, l_] := b[n, l] = If[n == 0, 1, Sum[b[n - 1, Append[Table[Max[l[[i]], j], {i, 2, Length[l]}], j]], {j, 1, l[[1]] + 1}]];
a[n_] := b[n, Table[0, 6]];
Table[a[n], {n, 0, 20}] (* Jean-François Alcover, May 27 2018, from Maple *)
CROSSREFS
Column k=6 of A287641.
Cf. A000110.
Sequence in context: A287586 A287279 A287257 * A099263 A366775 A192865
KEYWORD
nonn
AUTHOR
Alois P. Heinz, May 29 2017
STATUS
approved