OFFSET
0,2
FORMULA
a(n) = 1 - 4^n*Euler(n, 1/4).
Let p(n, x) = -x^n + Sum_{k=0..n} binomial(n,k)*Euler(k)*(x+1)^(n-k) (the polynomials defined in A162660), then a(n) = 2^n*p(n, 1/2).
MAPLE
seq(1 - 4^n*euler(n, 1/4), n=0..21);
MATHEMATICA
p := CoefficientList[Series[Exp[x z] Tanh[z], {z, 0, 21}], z];
norm := Table[2^n n!, {n, 0, 21}]; norm (p /. x -> 1/2)
CROSSREFS
KEYWORD
sign
AUTHOR
Peter Luschny, Jun 28 2019
STATUS
approved