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Generalized Euler number c(7,n).
6

%I #23 Oct 26 2024 23:36:42

%S 1,64,15872,9493504,10562158592,18878667833344,49488442978598912,

%T 178867627497727197184,852509723495811705208832,

%U 5180564635674867885905281024,39094622102339738427522497380352,358686739310560735577543742129700864,3931974790759726002374736527410407145472

%N Generalized Euler number c(7,n).

%H Matthew House, <a href="/A064068/b064068.txt">Table of n, a(n) for n = 0..180</a>

%H D. Shanks, <a href="http://dx.doi.org/10.1090/S0025-5718-1967-0223295-5">Generalized Euler and class numbers</a>. Math. Comp. 21 (1967) 689-694.

%H D. Shanks, <a href="http://dx.doi.org/10.1090/S0025-5718-1968-0227093-9">Corrigenda to: "Generalized Euler and class numbers"</a>, Math. Comp. 22 (1968), 699.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/EulerNumber.html">Euler Number</a>.

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

%p egf := sec(7*x)*(cos(x) + cos(3*x) - cos(5*x)): ser := series(egf, x, 24):

%p seq((2*n)!*coeff(ser, x, 2*n), n = 0..11); # _Peter Luschny_, Nov 21 2021

%t 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 *)

%Y Row 7 of A235605.

%Y Cf. A064072, A349266, A349264.

%K nonn,easy,changed

%O 0,2

%A _Eric W. Weisstein_, Aug 31 2001