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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

A001142 counts such paths of length n.

A000670 counts such paths under the inclusion relation.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..69

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

Cf. A000670, A001142.

Sequence in context: A172402 A297668 A203593 * A024041 A152554 A254430

Adjacent sequences:  A304899 A304900 A304901 * A304903 A304904 A304905

KEYWORD

nonn

AUTHOR

Geoffrey Critzer, May 20 2018

STATUS

approved

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Last modified August 8 05:50 EDT 2020. Contains 336290 sequences. (Running on oeis4.)