OFFSET
1,2
COMMENTS
The number of n-element posets that do not include the two 4-element posets "N" and "bowtie" as induced subposets.
LINKS
Stephan Wagner, Table of n, a(n) for n = 1..100
T. Hasebe and S. Tsujie, Order quasisymmetric functions distinguish rooted trees, arXiv:1610.03908 [math.CO], 2016-2017.
T. Hasebe and S. Tsujie, Order quasisymmetric functions distinguish rooted trees, Journal of Algebraic Combinatorics 46 (2017), 499-515.
V. Razanajatovo Misanantenaina and S. Wagner, A Tutte-like polynomial for rooted trees and specific posets, arXiv:1803.09623 [math.CO], 2018.
FORMULA
G.f. V(x) = 1 + x + 2x + 5x^2 + ... satisfies V(x) = (1-x)exp[sum_{m >=1} (2x^m-x^(2m))V(x^m)/m] (see Razanajatovo Misanantenaina/Wagner).
MATHEMATICA
V=1; Do[V = Normal[Series[(1 - x) Exp[Sum[(2 x^m - x^(2 m)) (V /. x -> x^m)/m, {m, 1, n}]], {x, 0, n}]], {n, 1, 20}]; Table[Coefficient[V, x, n], {n, 1, 20}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Stephan Wagner, Mar 28 2018
STATUS
approved