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

1, 1, 3, 12, 61, 375, 2699, 22232, 206086, 2122110, 24023623, 296474178, 3960532707, 56931074109, 876098828097, 14369369855760, 250215898045984, 4609913757678432, 89586669708676510, 1831372328505086980, 39284382532454768754, 882269612910279500214, 20703128006754726971507

Offset: 0

Author

Ilya Gutkovskiy, Jul 23 2018

Keywords

• nonn

Crossrefs

Cf. A001006, A086662, A086672, A317170.

Programs

Maple

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

Mathematica

nmax = 22; CoefficientList[Series[BesselI[1, 2 Log[1 - x]]/((1 - x) Log[1 - x]), {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[Abs[StirlingS1[n, k]] Hypergeometric2F1[(1 - k)/2, -k/2, 2, 4], {k, 0, n}], {n, 0, 22}]

Formula

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