OFFSET
0,4
COMMENTS
The rank of a poset is the number of cover relations in a maximal chain.
Equivalently, T(n,k) is the number of labeled posets P on [n] of rank at most one such that |image(P)| = k.
FORMULA
E.g.f.: Sum_{n>=0} x^n/n!*exp(y*x)^(2^n-1).
T(n,1) = A058877(n).
EXAMPLE
Triangle begins
1;
1;
1, 2;
1, 9, 3;
1, 28, 54, 4;
1, 75, 490, 270, 5;
1, 186, 3375, 6860, 1215, 6;
...
MATHEMATICA
nn = 9; Map[Select[#, # > 0 &] &, Table[n!, {n, 0, nn}] CoefficientList[Series[ Sum[ Exp[y x]^(2^n - 1) x^n/n!, {n, 0, nn}], {x, 0, nn}], {x, y}]] // Grid
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Geoffrey Critzer, Feb 05 2024
STATUS
approved