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Expansion of e.g.f. exp(x) / (2 - cos(x)).
1

%I #9 Oct 28 2021 02:07:51

%S 1,1,0,-2,2,26,-30,-622,982,25846,-50910,-1639142,3874862,147434366,

%T -406614390,-17851478062,56266545142,2799621404086,-9927225631470,

%U -552054087163382,2175042302117822,133686372253841006,-579383205000618150,-39002628245713951102

%N Expansion of e.g.f. exp(x) / (2 - cos(x)).

%F a(n) = Sum_{k=0..floor(n/2)} (-1)^k * binomial(n,2*k) * A094088(k).

%t nmax = 23; CoefficientList[Series[Exp[x]/(2 - Cos[x]), {x, 0, nmax}], x] Range[0, nmax]!

%o (PARI) my(x='x+O('x^40)); Vec(serlaplace(exp(x)/(2-cos(x)))) \\ _Michel Marcus_, Oct 24 2021

%Y Cf. A003701, A094088, A327034, A348580.

%K sign

%O 0,4

%A _Ilya Gutkovskiy_, Oct 24 2021