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Generalized Euler numbers, a(n) = n!*[x^n](sec(8*x)*2*(sin(4*x) + cos(4*x))).
5

%I #12 Oct 30 2024 12:15:24

%S 2,8,96,1408,29184,739328,22634496,806453248,32864600064,

%T 1506300919808,76717014122496,4297849713983488,262665886073094144,

%U 17390688314209599488,1239981021847665770496,94727563504456856240128,7719096548270543600615424,668321603392783694711226368

%N Generalized Euler numbers, a(n) = n!*[x^n](sec(8*x)*2*(sin(4*x) + cos(4*x))).

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

%H Matthew House, <a href="/A349267/b349267.txt">Table of n, a(n) for n = 0..353</a>

%p sec(8*x)*2*(sin(4*x) + cos(4*x)): series(%, x, 20): seq(n!*coeff(%, x, n), n = 0..17);

%t m = 17; CoefficientList[Series[2 * Sec[8*x] * (Sin[4*x] + Cos[4*x]), {x, 0, m}], x] * Range[0, m]! (* _Amiram Eldar_, Nov 21 2021 *)

%Y Row 8 of A349271.

%Y Bisections: A064069, A064073.

%Y Cf. A349264.

%K nonn,changed

%O 0,1

%A _Peter Luschny_, Nov 21 2021