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The denominators of the semiderivative of the Euler polynomials at x = 1 and normalized by sqrt(Pi).
3

%I #7 Aug 01 2021 12:57:37

%S 1,1,3,5,35,63,33,143,585,935,4199,399,35581,76475,11475,114057,13485,

%T 4023459,55825,6094011,16111095,12540957,122960435,467883,671993075,

%U 11586393,109938507,56448551,15260511805,3338985045,117979542989,25843026187,452039265909

%N The denominators of the semiderivative of the Euler 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 A346714 for formulas and references.

%p r := n -> int(diff(euler(n, x), x) / sqrt(1 - x), x = 0..1);

%p a := n -> denom(r(n)): seq(a(n), n = 0..23);

%p # Alternative:

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

%p seq(denom(simplify(subs(x=1, fe(n)))), n = 0..23);

%Y Cf. A346709, A346710, A346711, A346712, A346714 (numerator).

%K nonn,frac

%O 0,3

%A _Peter Luschny_, Jul 31 2021