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A326483 a(n) = 2^n*E2_{n}(1/2) with E2_{n} the polynomials defined in A326480.

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%I A326483 #17 Aug 24 2022 06:17:01
%S A326483 1,-2,-4,40,80,-1952,-3904,177280,354560,-25866752,-51733504,
%T A326483 5535262720,11070525440,-1633165156352,-3266330312704,635421069967360,
%U A326483 1270842139934720,-315212388819402752,-630424777638805504,194181169538675507200
%N A326483 a(n) = 2^n*E2_{n}(1/2) with E2_{n} the polynomials defined in A326480.
%C A326483 For comments see A326480.
%F A326483 From _Emanuele Munarini_, Aug 22 2022: (Start)
%F A326483 E.g.f. for the sequence of the absolute values: (1+tan(2*t))/cos(2*t).
%F A326483 |a(2*n)| = 2^(2*n) |E(2*n)|.
%F A326483 |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 A326483 # The function E2(n) is defined in A326480.
%p A326483 seq(subs(x=1/2, 2^n*E2(n)), n=0..22);
%Y A326483 Bisections (up to signs): A002436 (even), A000816 (odd).
%Y A326483 Cf. A326480, A155585, A326481, A326482, A326483, A326484.
%K A326483 sign
%O A326483 0,2
%A A326483 _Peter Luschny_, Jul 12 2019