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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.
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2
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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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FORMULA
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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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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]];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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