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%I #8 Nov 04 2014 03:00:58
%S 1,1,2,9,66,680,9255,159446,3369212,85259280,2535716685,87301792270,
%T 3436207077666,153006997872664,7639004900670507,424334306389160090,
%U 26050024400518079480,1756998299539728910624,129516073605566573413977
%N E.g.f.: 1 + Sum_{n>=1} x^n/n! * Product_{k=1..n} (exp(k*x)-1)/(exp(x)-1).
%H Vaclav Kotesovec, <a href="/A196193/b196193.txt">Table of n, a(n) for n = 0..160</a>
%e E.g.f.: A(x) = 1 + x + 2*x^2/2! + 9*x^3/3! + 66*x^4/4! + 680*x^5/5! +...
%e where
%e A(x) = 1 + x*(exp(x)-1)/(exp(x)-1) + x^2/2!*(exp(x)-1)*(exp(2*x)-1)/(exp(x)-1)^2 + x^3/3!*(exp(x)-1)*(exp(2*x)-1)*(exp(3*x)-1)/(exp(x)-1)^3 +...
%e Equivalently,
%e A(x) = 1 + x + x^2/2!*(exp(x)+1) + x^3/3!*(exp(x)+1)*(exp(2*x)+exp(x)+1) + x^4/4!*(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/m!*prod(k=1,m,(exp(k*x+x*O(x^n))-1)/(exp(x+x*O(x^n))-1))),n)}
%Y Cf. A196194.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Sep 28 2011
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