OFFSET
0,4
COMMENTS
See A309132 for background and conjectures.
FORMULA
a(n) = numerator(R(n+1)/4^mod(n,2)) with R(n) = n/(nB(n) + dB(n)/n) and nB(n) = numerator(B(n-1, 1/2)), dB(n) = denominator(B(n-1, 1/2)) where B(n, x) denotes the Bernoulli polynomials.
|a(2*n)| = A309132(2*n + 1) for n >= 0.
a(2*n+1) = (n + 1)^2 for n >= 0.
MAPLE
nB := n -> numer(bernoulli(n-1, 1/2)): dB := n -> denom(bernoulli(n-1, 1/2)):
R := n -> n/(nB(n) + dB(n)/n): a := n -> numer(R(n+1)/4^irem(n, 2)):
seq(a(n), n=0..58);
CROSSREFS
KEYWORD
sign
AUTHOR
Peter Luschny, Jul 15 2019
STATUS
approved