OFFSET
0,2
COMMENTS
For the numerators see A350669.
This sequence coincides with A025547(n+1), for n = 0, 1, ..., 37. See the comments there.
Thanks to Ralf Steiner for sending me a paper where this and similar sums appear.
LINKS
Hugo Pfoertner, Table of n, a(n) for n = 0..100
Milton Abramowitz and Irene A. Stegun, eds., Handbook of Mathematical Functions. p. 258, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy], p. 258.
Yue-Wu Li and Feng Qi, A New Closed-Form Formula of the Gauss Hypergeometric Function at Specific Arguments, Axioms (2024) Vol. 13, Art. No. 317. See p. 11 of 24.
FORMULA
a(n) = denominator((Psi(n+3/2) + gamma + 2*log(2))/2), with the Digamma function Psi(z), and the Euler-Mascheroni constant gamma = A001620. See Abramowitz-Stegun, p. 258, 6.3.4.
a(n) = denominator of ( 2*H_{2*n+2} - H_{n+1} ), where H_{n} is the n-th Harmonic number. - G. C. Greubel, Jul 24 2023
MATHEMATICA
With[{H=HarmonicNumber}, Table[Denominator[2*H[2n+2] -H[n+1]], {n, 0, 50}]] (* G. C. Greubel, Jul 24 2023 *)
PROG
(PARI) a(n) = denominator(sum(j=0, n, 1/(2*j+1))); \\ Michel Marcus, Mar 16 2022
(Magma) [Denominator((2*HarmonicNumber(2*n+2) - HarmonicNumber(n+1))): n in [0..40]]; // G. C. Greubel, Jul 24 2023
(SageMath) [denominator(2*harmonic_number(2*n+2, 1) - harmonic_number(n+1, 1)) for n in range(41)] # G. C. Greubel, Jul 24 2023
CROSSREFS
KEYWORD
nonn,frac,easy
AUTHOR
Wolfdieter Lang, Mar 16 2022
STATUS
approved