A309579 - OEIS

%I #26 Aug 24 2019 20:37:14

%S 2,6,22,102,582,3942,30822,272742,2691942,29303142,348637542,

%T 4499984742,62618845542,934401757542,14882928349542,252007880413542,

%U 4520257017565542,85616990623453542,1707551662741213542,35768179777214173542,785101998295619293542,18019779824218937053542

%N Maximum principal ratio of a strongly connected digraph on n nodes.

%C The principal ratio of a strongly connected digraph is the ratio of largest to smallest entries in the stationary distribution of a simple random walk on that digraph.

%H S. Aksoy, F. Chung, X. Peng, <a href="https://arxiv.org/abs/1602.01162">Extreme values of the stationary distribution of random walks on directed graphs</a>, arXiv:1602.01162 [math.CO], 2016.

%H S. Aksoy, F. Chung, X. Peng, <a href="https://doi.org/10.1016/j.aam.2016.06.012">Extreme values of the stationary distribution of random walks on directed graphs</a>, Advances in Applied Mathematics, 81:128--155, 2016.

%F a(n) = (2/3) * (n-1)! * ( n/(n-1) + (1/(n-1)!) * Sum_{i=1..n-3} i! ).

%F a(n) = 2 * A056199(n-1). - _Alois P. Heinz_, Aug 11 2019

%o (PARI) a(n) = (2/3) * (n-1)! * ( n/(n-1) + (1/(n-1)!) * sum(i=1, n-3, i!)); \\ _Michel Marcus_, Aug 11 2019

%Y Cf. A056199.

%K nonn

%O 3,1

%A _Sinan G. Aksoy_, Aug 08 2019