A349268 Generalized Euler numbers, a(n) = n!*[x^n](sec(9*x)*(4*sin(3*x) + 2)*cos(3*x)^2).

2, 12, 126, 2160, 49410, 1415232, 48649086, 1951153920, 89434106370, 4611775398912, 264235243691646, 16653520425185280, 1145011717430672130, 85285640517460180992, 6841110155700330881406, 587950108643300554506240, 53899295662946509072626690, 5249943672359370392053481472

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..348

Crossrefs

Row 9 of A349271.

Bisections: A064070, A064074.

Cf. A349264.

Programs

Maple

sec(9*x)*(4*sin(3*x) + 2)*cos(3*x)^2: series(%, x, 20): seq(n!*coeff(%, x, n), n = 0..17);

Mathematica

m = 17; CoefficientList[Series[Sec[9*x] * (4 * Sin[3*x] + 2) * Cos[3*x]^2, {x, 0, m}], x] * Range[0, m]! (* Amiram Eldar, Nov 21 2021 *)