A064069 Generalized Euler number c(8,n).

2, 96, 29184, 22634496, 32864600064, 76717014122496, 262665886073094144, 1239981021847665770496, 7719096548270543600615424, 61267211781784116552580202496, 603881788505747521507846892027904, 7236592671961544936200760521440362496, 103612803724706836868168667250308188995584

Offset: 0

Author

Eric W. Weisstein, Aug 31 2001

Keywords

• nonn
• easy

Links

• Matthew House, Table of n, a(n) for n = 0..176
• 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 8 of A235605.

Cf. A000281, A064073, A349267, A349264.

Programs

Maple

egf := sec(8*x)*2*cos(4*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[2 Sec[8 x] Cos[4 x], {x, 0, 24}], x^2] (* Matthew House, Oct 25 2024 *)

Formula

a(n) = 2^(4n+5) * A000281(n).

a(n) = (2*n)!*[x^(2*n)](sec(8*x)*2*cos(4*x)). - Peter Luschny, Nov 21 2021