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Generalized Euler numbers, a(n) = n!*[x^n](sec(7*x)*(-sin(2*x) + sin(4*x) + sin(6*x) + cos(x) + cos(3*x) - cos(5*x))).
5

%I #12 Oct 30 2024 12:16:19

%S 1,8,64,904,15872,355688,9493504,296327464,10562158592,423645846728,

%T 18878667833344,925434038426824,49488442978598912,2866986638191472168,

%U 178867627497727197184,11956421282992330042984,852509723495811705208832,64584221654333725499376008

%N Generalized Euler numbers, a(n) = n!*[x^n](sec(7*x)*(-sin(2*x) + sin(4*x) + sin(6*x) + cos(x) + cos(3*x) - cos(5*x))).

%C For references and cross references, compare the overview in A349264.

%H Matthew House, <a href="/A349266/b349266.txt">Table of n, a(n) for n = 0..360</a>

%p sec(7*x)*(-sin(2*x) + sin(4*x) + sin(6*x) + cos(x) + cos(3*x) - cos(5*x)): series(%, x, 20): seq(n!*coeff(%, x, n), n = 0..17);

%t m = 17; CoefficientList[Series[Sec[7*x] * (-Sin[2*x] + Sin[4*x] + Sin[6*x] + Cos[x] + Cos[3*x] - Cos[5*x]), {x, 0, m}], x] * Range[0, m]! (* _Amiram Eldar_, Nov 21 2021 *)

%Y Row 7 of A349271.

%Y Bisections: A064068, A064072.

%Y Cf. A349264.

%K nonn,changed

%O 0,2

%A _Peter Luschny_, Nov 21 2021