A343843 a(n) = Sum_{k=0..n} (-1)^k*binomial(n, k)*A000831(k).

1, -1, 1, -9, 33, -241, 1761, -15929, 161473, -1853281, 23584321, -330371049, 5047404513, -83546832721, 1489242229281, -28442492633369, 579425286625153, -12541705195066561, 287434687338368641, -6953491183101074889, 177069197398959999393, -4734481603905334522801

Offset: 0

Author

Peter Luschny, May 06 2021

Keywords

• sign

Crossrefs

Cf. A000831, A000834, A109449.

Programs

Maple

a := n -> add((-1)^k*binomial(n, k)*A000831(k), k=0..n):
seq(a(n), n = 0..21);

Mathematica

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 *)

Formula

a(n) = (-2)^n*Sum_{k=0..n} A109449(n, k)*(-1/2)^k.

From Vaclav Kotesovec, May 06 2021: (Start)

a(n) ~ (-1)^n * exp(-Pi/4) * 4^(n+1) * n! / Pi^(n+1).

E.g.f.: exp(x)*(1 - tan(x))/(1 + tan(x)). (End)