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%I #11 Nov 02 2014 05:04:00
%S 1,1,6,92,2760,134416,9626976,952336832,124374587520,20725471027456,
%T 4290994105591296,1080503158073449472,325167279095248865280,
%U 115252343303110680580096,47519237579074974018134016,22549702636577116941673152512,12202485589681663721911088087040
%N E.g.f.: Sum_{n>=0} Product_{k=1..n} tan((2*k-1)*x).
%H Vaclav Kotesovec, <a href="/A221080/b221080.txt">Table of n, a(n) for n = 0..150</a>
%F a(n) ~ sqrt(Pi) * 2^(n+1/2) * n^(2*n+1/2) / (exp(2*n) * G^(n+1/2)), where G = A006752 = 0.915965594177219... is Catalan's constant. - _Vaclav Kotesovec_, Nov 02 2014
%e E.g.f.: A(x) = 1 + x + 6*x^2/2! + 92*x^3/3! + 2760*x^4/4! + 134416*x^5/5! +...
%e where
%e A(x) = 1 + tan(x) + tan(x)*tan(3*x) + tan(x)*tan(3*x)*tan(5*x) + tan(x)*tan(3*x)*tan(5*x)*tan(7*x) + tan(x)*tan(3*x)*tan(5*x)*tan(7*x)*tan(9*x) +...
%o (PARI) {a(n)=local(X=x+x*O(x^n), Egf); Egf=sum(m=0, n, prod(k=1, m, tan((2*k-1)*X))); n!*polcoeff(Egf, n)}
%o for(n=0, 20, print1(a(n), ", "))
%Y Cf. A218260, A006752.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Dec 31 2012
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