OFFSET
0,3
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..200
Hsien-Kuei Hwang, Emma Yu Jin, Asymptotics and statistics on Fishburn matrices and their generalizations, arXiv:1911.06690 [math.CO], 2019.
FORMULA
From Vaclav Kotesovec, Oct 31 2014: (Start)
a(n) ~ 6*sqrt(2) * exp(Pi^2/24) * 12^n * n! / Pi^(2*n+2).
a(n) ~ exp(Pi^2/24) * 12^(n+1) * n^(n+1/2) / (exp(n) * Pi^(2*n+3/2)).
(End)
EXAMPLE
G.f.: A(x) = 1 + x + 4*x^2 + 16*x^3 + 77*x^4 + 460*x^5 + 3287*x^6 +...
such that, by definition,
A(x) = 1 + (1-(1-x))/(1-x) + (1-(1-x))*(1-(1-x)^3)/((1-x)*(1-x^3)) + (1-(1-x))*(1-(1-x)^3)*(1-(1-x)^5)/((1-x)*(1-x^3)*(1-x^5)) +...
PROG
(PARI) {a(n)=polcoeff(sum(m=0, n, prod(k=1, m, (1-(1-x)^(2*k-1))/(1-x^(2*k-1) +x*O(x^n)) )), n)}
for(n=0, 40, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Feb 19 2012
STATUS
approved