A262235 Denominators of a series leading to Euler's constant gamma.

4, 72, 32, 14400, 1728, 2540160, 138240, 261273600, 896000, 10538035200, 209018880, 407994402816000, 5633058816000, 941525544960000, 4723310592, 8707228239790080000, 6162712657920000, 17473102222724628480000, 107559878256230400000, 14162409169997856768000000

Offset

1,1

Comments

Gamma = 1 - 1/4 - 5/72 - 1/32 - 251/14400 - 19/1728 - 19087/2540160 - ..., see the references below.

Links

G. C. Greubel, Table of n, a(n) for n = 1..250

Iaroslav V. Blagouchine, Two series expansions for the logarithm of the gamma function involving Stirling numbers and containing only rational coefficients for certain arguments related to 1/pi, Journal of Mathematical Analysis and Applications (Elsevier), 2016. arXiv version, arXiv:1408.3902 [math.NT], 2014-2016.

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.

Formula

a(n) = C2(n)/(n*(n + 1)!), where C2(n) are Cauchy numbers of the second kind (see A002657 and A002790).

Example

Denominators of 1/4, 5/72, 1/32, 251/14400, 19/1728, 19087/2540160, ...

Maple

a := proc(n) local r; r := proc(n) option remember; if n=0 then 1 else
1 - add(r(k)/(n-k+1), k=0..n-1) fi end: denom(r(n)/(n*(n+1))) end:
seq(a(n), n=1..20); # Peter Luschny, Apr 19 2018

Mathematica

g[n_] := Sum[Abs[StirlingS1[n, l]]/(l + 1), {l, 1, n}]/(n*(n + 1)!); a[n_] := Denominator[g[n]]; Table[a[n], {n, 1, 20}]

Crossrefs

Cf. A001067, A001620, A002657, A002790, A006953, A075266, A075267, A195189.

Sequence in context: A088693 A322397 A333543 * A133003 A358293 A340917

Adjacent sequences: A262232 A262233 A262234 * A262236 A262237 A262238

Keyword

nonn,frac

Author

Iaroslav V. Blagouchine, Sep 15 2015

Status

approved