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E.g.f. satisfies: A'(x) = (cos(x) + sin(x)*A(x)) / (cos(x)*A(x) - sin(x)).
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%I #9 Jul 29 2014 14:01:51

%S 1,1,1,1,3,7,25,117,567,2931,20165,140169,1008691,8756711,80546609,

%T 736667037,7767188015,87947663355,983717687645,12138623741969,

%U 162832820098219,2156307692882095,30489019112863689,470349294170629989,7212155129160617511,114968617914648215939

%N E.g.f. satisfies: A'(x) = (cos(x) + sin(x)*A(x)) / (cos(x)*A(x) - sin(x)).

%C Note that a(88) is negative. - _Vaclav Kotesovec_, Jul 29 2014

%H Vaclav Kotesovec, <a href="/A245115/b245115.txt">Table of n, a(n) for n = 0..200</a>

%F E.g.f. satisfies:

%F (1) A(x) = (cos(x) + sin(x)*A'(x)) / (cos(x)*A'(x) - sin(x)).

%F (2) A(x) = 1 + Integral (cos(x) + sin(x)*A(x)) / (cos(x)*A(x) - sin(x)) dx.

%e E.g.f.: A(x) = 1 + x + x^2/2! + x^3/3! + 3*x^4/4! + 7*x^5/5! + 25*x^6/6! +...

%o (PARI) {a(n)=local(A=1+x,X=x+x*O(x^n));for(i=1,n,A=1+intformal((cos(X)+sin(X)*A)/(cos(X)*A-sin(X)+x*O(x^n))));n!*polcoeff(A,n)}

%o for(n=0,30,print1(a(n),", "))

%K sign

%O 0,5

%A _Paul D. Hanna_, Jul 29 2014