A346715 The denominators of the semiderivative of the Euler polynomials at x = 1 and normalized by sqrt(Pi).

1, 1, 3, 5, 35, 63, 33, 143, 585, 935, 4199, 399, 35581, 76475, 11475, 114057, 13485, 4023459, 55825, 6094011, 16111095, 12540957, 122960435, 467883, 671993075, 11586393, 109938507, 56448551, 15260511805, 3338985045, 117979542989, 25843026187, 452039265909

Offset

0,3

Comments

The semiderivative is the fractional derivative of order 1/2. The Davison-Essex method is used. See A346714 for formulas and references.

Links

Table of n, a(n) for n=0..32.

Maple

r := n -> int(diff(euler(n, x), x) / sqrt(1 - x), x = 0..1);
a := n -> denom(r(n)): seq(a(n), n = 0..23);
# Alternative:
fe := n -> sqrt(Pi)*fracdiff(euler(n, x), x, 1/2):
seq(denom(simplify(subs(x=1, fe(n)))), n = 0..23);

Crossrefs

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

Sequence in context: A162444 A305858 A261659 * A259853 A052468 A055786

Adjacent sequences: A346712 A346713 A346714 * A346716 A346717 A346718

Keyword

nonn,frac

Author

Peter Luschny, Jul 31 2021

Status

approved