A346710 The denominators of the semiderivative of the Bernoulli polynomials at x = 1 and normalized by sqrt(Pi).

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.

Links

Table of n, a(n) for n=0..29.

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

Adjacent sequences: A346707 A346708 A346709 * A346711 A346712 A346713

Keyword

nonn,frac

Author

Peter Luschny, Jul 31 2021

Status

approved