A348587 Expansion of e.g.f. exp(x) / (2 - cos(x)).

1, 1, 0, -2, 2, 26, -30, -622, 982, 25846, -50910, -1639142, 3874862, 147434366, -406614390, -17851478062, 56266545142, 2799621404086, -9927225631470, -552054087163382, 2175042302117822, 133686372253841006, -579383205000618150, -39002628245713951102

Offset: 0

Author

Ilya Gutkovskiy, Oct 24 2021

Keywords

• sign

Crossrefs

Cf. A003701, A094088, A327034, A348580.

Programs

Mathematica

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

PARI

my(x='x+O('x^40)); Vec(serlaplace(exp(x)/(2-cos(x)))) \\ Michel Marcus, Oct 24 2021

Formula

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