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%I #19 Mar 27 2019 10:01:51
%S 1,1,4,29,320,4741,88384,1988489,52448000,1587545161,54252120064,
%T 2066298252149,86799115489280,3986897970744781,198795278022098944,
%U 10694247962623751009,617392620634705756160,38074395493710549747601,2498063366053169206657024,173745719989547715852773069
%N Expansion of e.g.f. csc(x)*(1 - sqrt(1 - 4*sin(x)))/2.
%F E.g.f.: 1/(1 - sin(x)/(1 - sin(x)/(1 - sin(x)/(1 - sin(x)/(1 - ...))))), a continued fraction.
%F a(n) ~ sqrt(2) * 15^(1/4) * n^(n-1) / (exp(n) * (arcsin(1/4))^(n - 1/2)). - _Vaclav Kotesovec_, Nov 18 2017
%p a:=series(csc(x)*(1-sqrt(1-4*sin(x)))/2,x=0,20): seq(n!*coeff(a,x,n),n=0..19); # _Paolo P. Lava_, Mar 27 2019
%t nmax = 19; CoefficientList[Series[Csc[x] (1 - Sqrt[1 - 4 Sin[x]])/2, {x, 0, nmax}], x] Range[0, nmax]!
%t nmax = 19; CoefficientList[Series[1/(1 + ContinuedFractionK[-Sin[x], 1, {k, 1, nmax}]), {x, 0, nmax}], x] Range[0, nmax]!
%Y Cf. A000108, A195621, A295254, A295255, A295256, A295257, A295258.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Nov 18 2017
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