This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A262235 #32 Jun 29 2024 07:16:00
%S A262235 4,72,32,14400,1728,2540160,138240,261273600,896000,10538035200,
%T A262235 209018880,407994402816000,5633058816000,941525544960000,4723310592,
%U A262235 8707228239790080000,6162712657920000,17473102222724628480000,107559878256230400000,14162409169997856768000000
%N A262235 Denominators of a series leading to Euler's constant gamma.
%C A262235 Gamma = 1 - 1/4 - 5/72 - 1/32 - 251/14400 - 19/1728 - 19087/2540160 - ..., see the references below.
%H A262235 G. C. Greubel, <a href="/A262235/b262235.txt">Table of n, a(n) for n = 1..250</a>
%H A262235 Iaroslav V. Blagouchine, <a href="http://dx.doi.org/10.1016/j.jmaa.2016.04.032">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</a>, Journal of Mathematical Analysis and Applications (Elsevier), 2016. <a href="http://arxiv.org/abs/1408.3902">arXiv version</a>, arXiv:1408.3902 [math.NT], 2014-2016.
%H A262235 Iaroslav V. Blagouchine, <a href="http://dx.doi.org/10.1016/j.jnt.2015.06.012">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.</a> Journal of Number Theory (Elsevier), vol. 158, pp. 365-396, 2016. <a href="http://arxiv.org/abs/1501.00740">arXiv version</a>, arXiv:1501.00740 [math.NT], 2015.
%F A262235 a(n) = C2(n)/(n*(n + 1)!), where C2(n) are Cauchy numbers of the second kind (see A002657 and A002790).
%e A262235 Denominators of 1/4, 5/72, 1/32, 251/14400, 19/1728, 19087/2540160, ...
%p A262235 a := proc(n) local r; r := proc(n) option remember; if n=0 then 1 else
%p A262235 1 - add(r(k)/(n-k+1), k=0..n-1) fi end: denom(r(n)/(n*(n+1))) end:
%p A262235 seq(a(n), n=1..20); # _Peter Luschny_, Apr 19 2018
%t A262235 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}]
%Y A262235 Cf. A001067, A001620, A002657, A002790, A006953, A075266, A075267, A195189.
%K A262235 nonn,frac
%O A262235 1,1
%A A262235 _Iaroslav V. Blagouchine_, Sep 15 2015