A262383 Denominators of a semi-convergent series leading to the first Stieltjes constant gamma_1.
12, 720, 15120, 11200, 332640, 908107200, 4324320, 2940537600, 175991175360, 512143632000, 1427794368, 7795757249280, 107084577600, 279490747536000, 200143324310529600, 1178332991611776000, 157531148611200, 906996615309386784000, 5828652498614400, 262872227687509440000
Offset: 1
Examples
Denominators of -1/12, 11/720, -137/15120, 121/11200, -7129/332640, 57844301/908107200, ...
Links
- G. C. Greubel, Table of n, a(n) for n = 1..500
- Iaroslav V. Blagouchine, Expansions of generalized Euler's constants into the series of polynomials in 1/pi^2 and into the formal enveloping series with rational coefficients only. Journal of Number Theory (Elsevier), vol. 158, pp. 365-396, 2016. arXiv version, arXiv:1501.00740 [math.NT], 2015.
Crossrefs
Programs
-
Maple
a := n -> denom(Zeta(1 - 2*n)*(Psi(2*n) + gamma)): seq(a(n), n=1..20); # Peter Luschny, Apr 19 2018
-
Mathematica
a[n_] := Denominator[-BernoulliB[2*n]*HarmonicNumber[2*n - 1]/(2*n)]; Table[a[n], {n, 1, 20}] -
PARI
a(n) = denominator(-bernfrac(2*n)*sum(k=1,2*n-1,1/k)/(2*n)); \\ Michel Marcus, Sep 23 2015
Formula
a(n) = denominator(-B_{2n}*H_{2n-1}/(2n)), where B_n and H_n are Bernoulli and harmonic numbers respectively.
a(n) = denominator(Zeta(1 - 2*n)*(Psi(2*n) + gamma)), where gamma is Euler's gamma. - Peter Luschny, Apr 19 2018
Comments