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a(n) = 2^n*E2_{n}(1/2) with E2_{n} the polynomials defined in A326480.
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%I #17 Aug 24 2022 06:17:01

%S 1,-2,-4,40,80,-1952,-3904,177280,354560,-25866752,-51733504,

%T 5535262720,11070525440,-1633165156352,-3266330312704,635421069967360,

%U 1270842139934720,-315212388819402752,-630424777638805504,194181169538675507200

%N a(n) = 2^n*E2_{n}(1/2) with E2_{n} the polynomials defined in A326480.

%C For comments see A326480.

%F From _Emanuele Munarini_, Aug 22 2022: (Start)

%F E.g.f. for the sequence of the absolute values: (1+tan(2*t))/cos(2*t).

%F |a(2*n)| = 2^(2*n) |E(2*n)|.

%F |a(2*n+1)| = 2^(2*n+1) Sum_{k=0..n} binomial(2*n+1,2*k) |E(2*k)| T(n-k+1), where the E(n) are the Euler numbers (A122045) and the T(n) are the tangent numbers (A000182). (End)

%p # The function E2(n) is defined in A326480.

%p seq(subs(x=1/2, 2^n*E2(n)), n=0..22);

%Y Bisections (up to signs): A002436 (even), A000816 (odd).

%Y Cf. A326480, A155585, A326481, A326482, A326483, A326484.

%K sign

%O 0,2

%A _Peter Luschny_, Jul 12 2019