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A304902
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Let (P,<) be the strict partial order on the subsets of {1,2,...,n} ordered by their cardinality. Then a(n) is the number of paths of any length from {} to {1,2,...,n}.
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1
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1, 1, 3, 16, 175, 4356, 263424, 40144896, 15714084159, 15953234222500, 42223789335548788, 292262228709213966336, 5302397936652484482131200, 252622720869371754406993137664, 31660291085217875120800516475520000, 10454334647424614439930776175842716286976
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OFFSET
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0,3
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COMMENTS
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A001142 counts such paths of length n.
A000670 counts such paths under the inclusion relation.
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LINKS
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MAPLE
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b:= proc(n, k) option remember; `if`(k=0, 1,
add(b(n, j), j=0..k-1)*binomial(n, k))
end:
a:= n-> b(n$2):
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MATHEMATICA
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Table[f[list_] := Apply[Times, Map[Binomial[n, #] &, list]];
Total[Map[f, Map[Accumulate, Level[Map[Permutations, Partitions[n]], {2}]]]], {n, 0, 15}]
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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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