A348580 -id:A348580 - cp's OEIS frontend

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

Ilya Gutkovskiy, Oct 24 2021

sign

Cf. A003701, A094088, A327034, A348580.

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

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

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

A352906 Expansion of e.g.f. sinh(x) / (1 - sin(x)).

Original entry on oeis.org

0, 1, 2, 7, 24, 101, 472, 2507, 14784, 96361, 687392, 5332207, 44694144, 402663821, 3880880512, 39848805107, 434306095104, 5007757446481, 60907946680832, 779345606053207, 10465549612529664, 147168296199468341, 2162785172079204352, 33155700678534788507, 529311396083558989824

Offset: 0

Ilya Gutkovskiy, Apr 07 2022

nonn

Cf. A000111, A000667, A000795, A001250, A002084, A062161, A062272, A322623, A348580.

nmax = 24; CoefficientList[Series[Sinh[x]/(1 - Sin[x]), {x, 0, nmax}], x] Range[0, nmax]!

a(n) = Sum_{k=0..floor((n-1)/2)} binomial(n,2*k+1) * A000111(n-2*k).

a(n) ~ sinh(Pi/2) * 2^(n + 7/2) * n^(n + 3/2) / (exp(n) * Pi^(n + 3/2)). - Vaclav Kotesovec, Apr 07 2022

cp's OEIS Frontend

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

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