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 A317169 #8 Mar 27 2019 03:56:36
%S A317169 1,1,3,12,61,375,2699,22232,206086,2122110,24023623,296474178,
%T A317169 3960532707,56931074109,876098828097,14369369855760,250215898045984,
%U A317169 4609913757678432,89586669708676510,1831372328505086980,39284382532454768754,882269612910279500214,20703128006754726971507
%N A317169 Expansion of e.g.f. BesselI(1,2*log(1 - x))/((1 - x)*log(1 - x)).
%F A317169 a(n) = Sum_{k=0..n} |Stirling1(n,k)|*A001006(k).
%p A317169 a:=series(BesselI(1,2*log(1 - x))/((1 - x)*log(1 - x)), x=0, 23): seq(n!*coeff(a, x, n), n=0..22); # _Paolo P. Lava_, Mar 26 2019
%t A317169 nmax = 22; CoefficientList[Series[BesselI[1, 2 Log[1 - x]]/((1 - x) Log[1 - x]), {x, 0, nmax}], x] Range[0, nmax]!
%t A317169 Table[Sum[Abs[StirlingS1[n, k]] Hypergeometric2F1[(1 - k)/2, -k/2, 2, 4], {k, 0, n}], {n, 0, 22}]
%Y A317169 Cf. A001006, A086662, A086672, A317170.
%K A317169 nonn
%O A317169 0,3
%A A317169 _Ilya Gutkovskiy_, Jul 23 2018