OFFSET
1,4
COMMENTS
Except for the initial 0, these are the absolute values of A349719. - Ira M. Gessel, Nov 01 2023
LINKS
Richard P. Stanley, Hyperplane arrangements, interval orders, and trees, Proc. Natl. Acad. Sci. USA 93 (1996), 2620-2625.
Vasu Tewari, Gessel polynomials, rooks, and extended Linial arrangements, arXiv preprint arXiv:1604.06894 [math.CO], 2016.
FORMULA
From Ira M. Gessel, Nov 01 2023: (Start)
a(n) = (1/2^n) * Sum_{k=0..n} (k-1)^(n-1) * binomial(n,k) for n>=2.
In the following generating functions we take a(1)=1 rather than a(1)=0.
E.g.f.: 1 + (1/2)*x/LambertW(-(1/2)*x*exp(x/2)).
E.g.f.: 1-1/B(x), where B(x) is the e.g.f. of A007889. See Corollary 4.2 of Stanley's paper. (End)
a(n) ~ sqrt(1 + LambertW(exp(-1))) * n^(n-1) / (exp(n) * 2^n * LambertW(exp(-1))^(n-1)). - Vaclav Kotesovec, Nov 13 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Mar 19 2017
EXTENSIONS
More terms from Ira M. Gessel, Nov 01 2023
STATUS
approved