A349265 Generalized Euler numbers, a(n) = n!*[x^n](sec(5*x)*(sin(x) + sin(3*x) + cos(2*x) + cos(4*x))).

2, 4, 30, 272, 3522, 55744, 1066590, 23750912, 604935042, 17328937984, 551609685150, 19313964388352, 737740947722562, 30527905292468224, 1360427147514751710, 64955605537174126592, 3308161927353377294082, 179013508069217017790464, 10256718523496425979562270

Offset: 0

Author

Peter Luschny, Nov 20 2021

Keywords

• nonn

Comments

For references and examples see A349264.

Links

• Matthew House, Table of n, a(n) for n = 0..377

Crossrefs

Row 5 of A349271.

Cf. A000111, A001589, A007289, A349264, A001587.

Programs

Mathematica

m = 18; CoefficientList[Series[Sec[5*x] * (Sin[x] + Sin[3*x] + Cos[2*x] + Cos[4*x]), {x, 0, m}], x] * Range[0, m]! (* Amiram Eldar, Nov 20 2021 *)

PARI

seq(n)={my(x='x + O('x^(n+1))); Vec(serlaplace((sin(x) + sin(3*x) + cos(2*x) + cos(4*x))/cos(5*x)))} \\ Andrew Howroyd, Nov 20 2021

Sage

t = PowerSeriesRing(QQ, 't', default_prec=19).gen()
f = (sin(t) + sin(3*t) + cos(2*t) + cos(4*t)) / cos(5*t)
f.egf_to_ogf().list()