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A201158 E.g.f. exp(x)/(cos(x) - sin(x)).

%I A201158 #34 Jan 20 2024 19:41:00
%S A201158 1,2,6,24,124,792,6056,53984,549904,6301472,80233056,1123714944,
%T A201158 17169102784,284184941952,5065697161856,96747688891904,
%U A201158 1970927736619264,42660873261343232,977715195437139456,23652447354912036864,602304626050881977344
%N A201158 E.g.f. exp(x)/(cos(x) - sin(x)).
%C A201158 Sum_{n>=0} a(n)x^n/n! = exp(x)/(cos(x) - sin(x)).
%F A201158 Sum_{n>=0} a(n)x^n/n! = exp(x)/(cos(x) - sin(x)).
%F A201158 exp(x)/(cos(x) - sin(x)) = 1/G(0); G(k) = 1-2*x/(4*k+1+x*(4*k+1)/(2*(2*k+1)-x-2*(x^2)*(2*k+1)/((x^2)-(2*k+2)*(4*k+3)/G(k+1)))); (continued fraction).
%F A201158 G.f.: 1/G(0) where G(k) = 1 - 2*x*(k+1) - 2*x^2*(k+1)^2/G(k+1); (continued fraction). - _Sergei N. Gladkovskii_, Jan 12 2013
%F A201158 a(n) ~ n! * exp(Pi/4)*2^(2*n+3/2)/Pi^(n+1). - _Vaclav Kotesovec_, Jun 27 2013
%F A201158 G.f.: T(0)/(1-2*x), where T(k) = 1 - 2*x^2*(k+1)^2/(2*x^2*(k+1)^2 - (1 - 2*x - 2*x*k)*(1 - 4*x - 2*x*k)/T(k+1) ); (continued fraction). - _Sergei N. Gladkovskii_, Oct 29 2013
%p A201158 A:=series(exp(x)/(cos(x)-sin(x)),x,40);
%p A201158 G(x):=A : f[0]:=G(x): for n from 1 to 41 do f[n]:=diff(f[n-1], x) od: x:=0: seq(f[n], n=0..40);
%t A201158 nn = 30; Range[0, nn]! CoefficientList[Series[Exp[x]/(Cos[x] - Sin[x]), {x, 0, nn}], x] (* _T. D. Noe_, Dec 05 2011 *)
%K A201158 nonn
%O A201158 0,2
%A A201158 _Sergei N. Gladkovskii_, Nov 27 2011