A349266 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))).

1, 8, 64, 904, 15872, 355688, 9493504, 296327464, 10562158592, 423645846728, 18878667833344, 925434038426824, 49488442978598912, 2866986638191472168, 178867627497727197184, 11956421282992330042984, 852509723495811705208832, 64584221654333725499376008

Offset: 0

Author

Peter Luschny, Nov 21 2021

Keywords

• nonn

Comments

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

Links

• Matthew House, Table of n, a(n) for n = 0..360

Crossrefs

Row 7 of A349271.

Bisections: A064068, A064072.

Cf. A349264.

Programs

Maple

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);

Mathematica

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 *)