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%I #13 Feb 05 2020 23:52:04
%S 1,1,4,42,804,24200,1052310,62399232,4838470280,475205921136,
%T 57651242228010,8466308935131080,1480085055633108012,
%U 303741049766220682200,72304996099042631680574,19761618044081811015046320,6145897155031392768635838480
%N E.g.f.: 1 + Sum_{n>=1} x^n * Product_{k=1..n} (exp(k*x)-1)/(exp(x)-1).
%H Vaclav Kotesovec, <a href="/A196194/b196194.txt">Table of n, a(n) for n = 0..160</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) ~ 12^(n+1) * n^(2*n+1) / (exp(2*n) * Pi^(2*n+1)). - _Vaclav Kotesovec_, Nov 04 2014
%e E.g.f.: A(x) = 1 + x + 4*x^2/2! + 42*x^3/3! + 804*x^4/4! + 24200*x^5/5! + ...
%e where
%e A(x) = 1 + x*(exp(x)-1)/(exp(x)-1) + x^2*(exp(x)-1)*(exp(2*x)-1)/(exp(x)-1)^2 + x^3*(exp(x)-1)*(exp(2*x)-1)*(exp(3*x)-1)/(exp(x)-1)^3 + ...
%e Equivalently,
%e A(x) = 1 + x + x^2*(exp(x)+1) + x^3*(exp(x)+1)*(exp(2*x)+exp(x)+1) + x^4*(exp(x)+1)*(exp(2*x)+exp(x)+1)*(exp(3*x)+exp(2*x)+exp(x)+1) + ...
%o (PARI) {a(n)=n!*polcoeff(1+sum(m=1,n,x^m*prod(k=1,m,(exp(k*x+x*O(x^n))-1)/(exp(x+x*O(x^n))-1))),n)}
%Y Cf. A196193.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Sep 28 2011
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