%I #13 May 06 2021 12:21:34
%S 1,-1,1,-9,33,-241,1761,-15929,161473,-1853281,23584321,-330371049,
%T 5047404513,-83546832721,1489242229281,-28442492633369,
%U 579425286625153,-12541705195066561,287434687338368641,-6953491183101074889,177069197398959999393,-4734481603905334522801
%N a(n) = Sum_{k=0..n} (-1)^k*binomial(n, k)*A000831(k).
%F a(n) = (-2)^n*Sum_{k=0..n} A109449(n, k)*(-1/2)^k.
%F From _Vaclav Kotesovec_, May 06 2021: (Start)
%F a(n) ~ (-1)^n * exp(-Pi/4) * 4^(n+1) * n! / Pi^(n+1).
%F E.g.f.: exp(x)*(1 - tan(x))/(1 + tan(x)). (End)
%p a := n -> add((-1)^k*binomial(n, k)*A000831(k), k=0..n):
%p seq(a(n), n = 0..21);
%t Table[-1 + Sum[(-1)^k * Binomial[n, k] * 4^k * Abs[EulerE[k,1/2] + EulerE[k,1]], {k,0,n}], {n,0,20}] (* _Vaclav Kotesovec_, May 06 2021 *)
%Y Cf. A000831, A000834, A109449.
%K sign
%O 0,4
%A _Peter Luschny_, May 06 2021
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