login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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