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%I #12 Feb 07 2020 13:39:32
%S 1,1,2,15,143,1552,18282,228174,2976534,40256580,561755676,8066942027,
%T 119104886610,1809118800204,28327453520403,458854209551159,
%U 7727223037965079,136130623466875012,2526349854311842166,49724570281877830993,1043539871136604436514,23417606258398828845811
%N G.f.: A(x) = 1+x + Sum_{n>=2} Product_{k=1..n} (A(x)^k - 1).
%H Vaclav Kotesovec, <a href="/A224885/b224885.txt">Table of n, a(n) for n = 0..125</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.
%e G.f.: A(x) = 1 + x + 2*x^2 + 15*x^3 + 143*x^4 + 1552*x^5 + 18282*x^6 +...
%e where
%e A(x) = 1+x + (A(x)-1)*(A(x)^2-1) + (A(x)-1)*(A(x)^2-1)*(A(x)^3-1) + (A(x)-1)*(A(x)^2-1)*(A(x)^3-1)*(A(x)^4-1) + (A(x)-1)*(A(x)^2-1)*(A(x)^3-1)*(A(x)^4-1)*(A(x)^5-1) +...
%o (PARI) {a(n)=local(A=1+x);for(i=1,n,A=1+x+sum(k=2,n,prod(j=1,k,A^j-1 +x*O(x^n))));polcoeff(A,n)}
%o for(n=0,20,print1(a(n),", "))
%Y Cf. A186737, A227619.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Aug 22 2013
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