%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