%I #6 Aug 01 2021 12:57:19

%S 1,1,3,5,105,63,77,6435,6435,663,24871,1322685,45885,68425,294975,

%T 1479,4083810885,46725525,46940355,80555475,509285205,471824925,

%U 5147492805,116197611075,3848337675,111954046295,46499760153,21364716527,1238763451695,149973995325

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

%C The semiderivative is the fractional derivative of order 1/2. The Davison-Essex method is used. See A346709 for formulas and references.

%p r := n -> int(diff(bernoulli(n, t), t) / sqrt(1 - t), t = 0..1):

%p a := n -> denom(r(n)): seq(a(n), n = 0..9);

%p # Alternative:

%p fb := n -> sqrt(Pi)*fracdiff(bernoulli(n, x), x, 1/2):

%p seq(denom(simplify(subs(x=1, fb(n)))), n = 0..9);

%Y Cf. A346709 (numerator), A346711, A346712, A346714, A346715.

%K nonn,frac

%O 0,3

%A _Peter Luschny_, Jul 31 2021