OFFSET
0,3
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..310
Hsien-Kuei Hwang, Emma Yu Jin, Asymptotics and statistics on Fishburn matrices and their generalizations, arXiv:1911.06690 [math.CO], 2019.
FORMULA
a(n) ~ 2*exp(Pi^2/12) * 6^(n+3/2) * n^(n+1) / (exp(n) * Pi^(2*n+2)). - Vaclav Kotesovec, Oct 31 2014
EXAMPLE
G.f.: A(x) = 1 + x + 3*x^2 + 8*x^3 + 25*x^4 + 83*x^5 + 323*x^6 +...
such that, by definition,
A(x) = 1 + (1-(1-x))/(1-x) + (1-(1-x))*(1-(1-x)^2)/((1-x)*(1-x^2)) + (1-(1-x))*(1-(1-x)^2)*(1-(1-x)^3)/((1-x)*(1-x^2)*(1-x^3)) +...
PROG
(PARI) {a(n)=polcoeff(sum(m=0, n, prod(k=1, m, (1-(1-x)^k)/(1-x^k +x*O(x^n)) )), n)}
for(n=0, 25, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Feb 19 2012
STATUS
approved