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%I #18 Feb 07 2020 13:37:50
%S 1,1,3,8,25,83,323,1410,7062,39660,248287,1709505,12843315,104446836,
%T 913968191,8560027375,85427505885,904899664970,10139054456975,
%U 119802780498730,1488769376468607,19409525611304801,264890181139521141,3776619220990535910
%N G.f.: Sum_{n>=0} Product_{k=1..n} (1 - (1-x)^k)/(1 - x^k).
%H Vaclav Kotesovec, <a href="/A207651/b207651.txt">Table of n, a(n) for n = 0..310</a>
%H Hsien-Kuei Hwang, Emma Yu Jin, <a href="https://arxiv.org/abs/1911.06690">Asymptotics and statistics on Fishburn matrices and their generalizations</a>, arXiv:1911.06690 [math.CO], 2019.
%F 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
%e G.f.: A(x) = 1 + x + 3*x^2 + 8*x^3 + 25*x^4 + 83*x^5 + 323*x^6 +...
%e such that, by definition,
%e 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)) +...
%o (PARI) {a(n)=polcoeff(sum(m=0,n,prod(k=1,m,(1-(1-x)^k)/(1-x^k +x*O(x^n)) )),n)}
%o for(n=0,25,print1(a(n),", "))
%Y Cf. A207652, A207653, A207654, A193548.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Feb 19 2012