Revision History for A287670
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| A287670
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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-7 is member of a block >= b-1.
(history;
published version)
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#9 by Michel Marcus at Sun May 27 10:33:25 EDT 2018
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#8 by Joerg Arndt at Sun May 27 10:18:07 EDT 2018
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#7 by Jean-François Alcover at Sun May 27 09:26:51 EDT 2018
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#6 by Jean-François Alcover at Sun May 27 09:26:48 EDT 2018
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| MATHEMATICA
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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, 7]];
Table[a[n], {n, 0, 20}] (* Jean-François Alcover, May 27 2018, from Maple *)
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approved
editing
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#5 by Alois P. Heinz at Mon May 29 20:43:12 EDT 2017
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#4 by Alois P. Heinz at Mon May 29 20:43:08 EDT 2017
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| LINKS
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Alois P. Heinz, <a href="/A287670/b287670.txt">Table of n, a(n) for n = 0..37</a>
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| STATUS
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approved
editing
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#3 by Alois P. Heinz at Mon May 29 17:37:24 EDT 2017
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#2 by Alois P. Heinz at Mon May 29 17:36:03 EDT 2017
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| NAME
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allocated for Alois P. Heinz
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-7 is member of a block >= b-1.
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| DATA
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1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115974, 678434, 4209827, 27578206, 189954361, 1370870811, 10334533723, 81166980407, 662588540048, 5610196619724, 49177794178940, 445536788068643, 4165402700226511, 40131393651398259, 397935154986242021
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| OFFSET
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0,3
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| LINKS
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Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
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| FORMULA
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a(n) = A287641(n,7).
a(n) = A000110(n) for n <= 9.
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| EXAMPLE
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a(10) = 115974 = 115975 - 1 = A000110(10) - 1 counts all set partitions of [10] except: 13456789|2|(10).
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| MAPLE
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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$7]):
seq(a(n), n=0..20);
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| CROSSREFS
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Column k=7 of A287641.
Cf. A000110.
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| KEYWORD
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allocated
nonn
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| AUTHOR
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Alois P. Heinz, May 29 2017
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approved
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#1 by Alois P. Heinz at Mon May 29 15:12:17 EDT 2017
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| NAME
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allocated for Alois P. Heinz
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| KEYWORD
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allocated
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| STATUS
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approved
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