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%I #7 Nov 02 2014 13:11:09
%S 1,1,2,8,64,696,9872,191008,4566784,131276032,4579799552,186766023168,
%T 8790216177664,476464164850688,29213015354673152,2012710664900415488,
%U 155075844379301576704,13231714749051132248064,1244975006293271728750592
%N E.g.f.: Sum_{n>=0} (1/n!) * Product_{k=1..n} tan(k*x).
%H Vaclav Kotesovec, <a href="/A193549/b193549.txt">Table of n, a(n) for n = 0..150</a>
%e A(x) = 1 + x + 2*x^2/2! + 8*x^3/3! + 64*x^4/4! + 696*x^5/5! + 9872*x^6/6! +...
%e where
%e A(x) = 1 + tan(x) + tan(x)*tan(2*x)/2! + tan(x)*tan(2*x)*tan(3*x)/3! +...
%o (PARI) {a(n)=local(X=x+x*O(x^n), Egf); Egf=sum(m=0, n, prod(k=1, m, tan(k*X))/m!); n!*polcoeff(Egf, n)}
%K nonn
%O 0,3
%A _Paul D. Hanna_, Jul 30 2011
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