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 A317169 Expansion of e.g.f. BesselI(1,2*log(1 - x))/((1 - x)*log(1 - x)). 1

%I

%S 1,1,3,12,61,375,2699,22232,206086,2122110,24023623,296474178,

%T 3960532707,56931074109,876098828097,14369369855760,250215898045984,

%U 4609913757678432,89586669708676510,1831372328505086980,39284382532454768754,882269612910279500214,20703128006754726971507

%N Expansion of e.g.f. BesselI(1,2*log(1 - x))/((1 - x)*log(1 - x)).

%F a(n) = Sum_{k=0..n} |Stirling1(n,k)|*A001006(k).

%p 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 nmax = 22; CoefficientList[Series[BesselI[1, 2 Log[1 - x]]/((1 - x) Log[1 - x]), {x, 0, nmax}], x] Range[0, nmax]!

%t Table[Sum[Abs[StirlingS1[n, k]] Hypergeometric2F1[(1 - k)/2, -k/2, 2, 4], {k, 0, n}], {n, 0, 22}]

%Y Cf. A001006, A086662, A086672, A317170.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Jul 23 2018

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Last modified November 29 23:37 EST 2020. Contains 338780 sequences. (Running on oeis4.)