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A346710
The denominators of the semiderivative of the Bernoulli polynomials at x = 1 and normalized by sqrt(Pi).
3
1, 1, 3, 5, 105, 63, 77, 6435, 6435, 663, 24871, 1322685, 45885, 68425, 294975, 1479, 4083810885, 46725525, 46940355, 80555475, 509285205, 471824925, 5147492805, 116197611075, 3848337675, 111954046295, 46499760153, 21364716527, 1238763451695, 149973995325
OFFSET
0,3
COMMENTS
The semiderivative is the fractional derivative of order 1/2. The Davison-Essex method is used. See A346709 for formulas and references.
MAPLE
r := n -> int(diff(bernoulli(n, t), t) / sqrt(1 - t), t = 0..1):
a := n -> denom(r(n)): seq(a(n), n = 0..9);
# Alternative:
fb := n -> sqrt(Pi)*fracdiff(bernoulli(n, x), x, 1/2):
seq(denom(simplify(subs(x=1, fb(n)))), n = 0..9);
CROSSREFS
Cf. A346709 (numerator), A346711, A346712, A346714, A346715.
Sequence in context: A103081 A338269 A371194 * A234600 A003112 A130187
KEYWORD
nonn,frac
AUTHOR
Peter Luschny, Jul 31 2021
STATUS
approved