A064068 Generalized Euler number c(7,n).

1, 64, 15872, 9493504, 10562158592, 18878667833344, 49488442978598912, 178867627497727197184, 852509723495811705208832, 5180564635674867885905281024, 39094622102339738427522497380352, 358686739310560735577543742129700864, 3931974790759726002374736527410407145472

Offset: 0

Author

Eric W. Weisstein, Aug 31 2001

Keywords

• nonn
• easy

Links

• Matthew House, Table of n, a(n) for n = 0..180
• D. Shanks, Generalized Euler and class numbers. Math. Comp. 21 (1967) 689-694.
• D. Shanks, Corrigenda to: "Generalized Euler and class numbers", Math. Comp. 22 (1968), 699.
• Eric Weisstein's World of Mathematics, Euler Number.

Crossrefs

Row 7 of A235605.

Cf. A064072, A349266, A349264.

Programs

Maple

egf := sec(7*x)*(cos(x) + cos(3*x) - cos(5*x)): ser := series(egf, x, 24):
seq((2*n)!*coeff(ser, x, 2*n), n = 0..11); # Peter Luschny, Nov 21 2021

Mathematica

Range[0, 24, 2]! CoefficientList[Series[Sec[7 x] (Cos[x] + Cos[3 x] - Cos[5 x]), {x, 0, 24}], x^2] (* Matthew House, Oct 25 2024 *)

Formula

a(n) = (2*n)!*[x^(2*n)](sec(7*x)*(cos(x) + cos(3*x) - cos(5*x))). - Peter Luschny, Nov 21 2021