OFFSET
0
LINKS
Madeline Beals-Reid, A Quadratic Relation in the Bernoulli Numbers, The Pump Journal of Undergraduate Research, 6 (2023), 29-39.
FORMULA
Let B(x) = x/(1 - exp(-x)), the e.g.f. of the Bernoulli numbers with B(1) = 1/2.
a(n) = signum([x^n] B(x)^2)) = signum([x^n] z^2 / (exp(-z) - 1)^2).
a(n) = signum([x^n] (x + 1)*B(x) - x*B'(x)).
MAPLE
ogf := (2*z^4 + 2*z^3 + 2*z^2 + z + 1)/(z^2 + 1):
ser := series(ogf, z, 100): seq(coeff(ser, z, n), n = 0..74);
CROSSREFS
KEYWORD
sign
AUTHOR
Peter Luschny, Jan 23 2023
STATUS
approved