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A304902
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}.
1
1, 1, 3, 16, 175, 4356, 263424, 40144896, 15714084159, 15953234222500, 42223789335548788, 292262228709213966336, 5302397936652484482131200, 252622720869371754406993137664, 31660291085217875120800516475520000, 10454334647424614439930776175842716286976
OFFSET
0,3
COMMENTS
A001142 counts such paths of length n.
A000670 counts such paths under the inclusion relation.
LINKS
MAPLE
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):
seq(a(n), n=0..17); # Alois P. Heinz, May 20 2018
MATHEMATICA
Table[f[list_] := Apply[Times, Map[Binomial[n, #] &, list]];
Total[Map[f, Map[Accumulate, Level[Map[Permutations, Partitions[n]], {2}]]]], {n, 0, 15}]
CROSSREFS
Sequence in context: A172402 A297668 A203593 * A024041 A152554 A254430
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, May 20 2018
STATUS
approved