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A287666
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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-3 is member of a block >= b-1.
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2
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1, 1, 2, 5, 15, 52, 202, 861, 3970, 19596, 102703, 567867, 3295439, 19986462, 126231946, 827759525, 5621051650, 39439867696, 285368007479, 2125566382124, 16273261632111, 127881070062521, 1030221084660031, 8498826714433335, 71721238761675612, 618573094313147709
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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(6) = 202 = 203 - 1 = A000110(6) - 1 counts all set partitions of [6] except: 1345|2|6.
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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$3]):
seq(a(n), n=0..26);
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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, {0, 0, 0}];
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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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