A369921 Number of cover relations summed over the rank-1 labeled posets on [n].

0, 0, 2, 18, 204, 2940, 56670, 1471806, 52067512, 2520298584, 167850357210, 15435027907530, 1967345286257604, 348527628228821652, 86057693880611800438, 29677160119074814383030, 14321851348104417100842480

Offset

0,3

Comments

The rank of a poset is the number of cover relations in a maximal chain.

A cover relation in a poset is an ordered pair x <= y such that there is no z with x <= z <= y.

Links

Table of n, a(n) for n=0..16.

Eric Weisstein's World of Mathematics, Cover Relation.

Formula

a(n) = Sum_{k=1..floor(n^2/4)} A052296(n,k)*k.

Mathematica

nn = 16; Table[Table[n!, {n, 0, nn}] CoefficientList[D[Series[Sum[Exp[y x]^Binomial[n, i]*Exp[  x]^(2^n - Binomial[n, i] - 1)  x^n/n!, {n, 0, nn}], {x, 0, nn}], y] /. y -> 1, x]*i, {i, 1, nn - 1}] // Total

Crossrefs

Cf. A001831, A369919, A052296.

Sequence in context: A266518 A303381 A224881 * A092882 A123855 A121407

Adjacent sequences: A369918 A369919 A369920 * A369922 A369923 A369924

Keyword

nonn

Author

Geoffrey Critzer, Feb 05 2024

Status

approved