

A001833


Number of labeled graded partially ordered sets with n elements.
(Formerly M3067 N1243)


10



1, 1, 3, 19, 219, 3991, 106623, 3964339, 199515459, 13399883551, 1197639892983, 143076298623259, 23053861370437659, 5062745845287855271, 1530139311543346178223, 641441466132460086890179, 375107113287994040621904819, 307244526491924695346004951151, 353511145615118063468292270299943
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OFFSET

0,3


COMMENTS

Here "graded" means that there exists a rank function rk from the poset to the integers such that whenever v covers w in the poset, we have rk(v) = rk(w) + 1. Note that this notion of grading is weaker than in sequence A006860, which counts posets in which all maximal chains have the same length.


REFERENCES

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


LINKS



EXAMPLE

The poset on {a, b, c, d, e} defined by the relations a < b < c and d < e is counted by this sequence. (For example, one associated rank function is rk(a) = rk(d) = 0, rk(b) = rk(e) = 1 and rk(c) = 2.) However, the poset defined by the relations a < b < c and a < d < e < c is not graded and so not counted by this sequence.


PROG

(PARI) \\ C(n) is defined in A361951.
seq(n)={my(c=C(n)); Vec(serlaplace(c[n+1]/c[n]))} \\ Andrew Howroyd, Mar 31 2023


CROSSREFS

Graded posets with no chain of length 3 are counted by A001831.


KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



