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Matrix product of triangle of Stirling numbers of second kind A008277 and square of unsigned Lah triangle A105278.
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%I #15 Aug 11 2019 00:03:59

%S 1,5,1,37,15,1,365,223,30,1,4501,3675,745,50,1,66605,68071,18450,1865,

%T 75,1,1149877,1411515,479101,64750,3920,105,1,22687565,32512663,

%U 13260030,2244501,181650,7322,140,1,503589781,825175275,393017185,79948050,8103711,436590,12558,180,1

%N Matrix product of triangle of Stirling numbers of second kind A008277 and square of unsigned Lah triangle A105278.

%C Also the number of k-dimensional flats of the extended Catalan arrangement of dimension n consisting of hyperplanes x_i - x_j = d (1 <= i < j <= n, -2 <= d <= 2).

%H Robert Gill, <a href="https://doi.org/10.1016/S0012-365X(97)00187-8">The number of elements in a generalized partition semilattice</a>, Discrete mathematics 186.1-3 (1998): 125-134.

%H N. Nakashima and S. Tsujie, <a href="https://arxiv.org/abs/1904.09748">Enumeration of Flats of the Extended Catalan and Shi Arrangements with Species</a>, arXiv:1904.09748 [math.CO], 2019.

%F E.g.f.: exp((exp(x)-1)*y/(3-2exp(x))).

%e Triangle begins:

%e 1;

%e 5, 1;

%e 37, 15, 1;

%e 365, 223, 30, 1;

%e 4501, 3675, 745, 50, 1;

%e ...

%Y Cf. A008277, A105278, A050351 (first column), A109092 (row sums).

%K nonn,tabl

%O 1,2

%A _Shuhei Tsujie_, May 27 2019