cp's OEIS Frontend

A308281 The third power of the unsigned Lah triangular matrix A105278.

%I A308281 #13 Jul 27 2019 16:00:19
%S A308281 1,6,1,54,18,1,648,324,36,1,9720,6480,1080,60,1,174960,145800,32400,
%T A308281 2700,90,1,3674160,3674160,1020600,113400,5670,126,1,88179840,
%U A308281 102876480,34292160,4762800,317520,10584,168,1,2380855680,3174474240,1234517760,205752960,17146080,762048,18144,216,1
%N A308281 The third power of the unsigned Lah triangular matrix A105278.
%C A308281 Also the number of k-dimensional flats of the extended Shi arrangement of dimension n consisting of hyperplanes x_i - x_j = d (1 <= i < j <= n, -2 <= d <= 3).
%H A308281 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 A308281 E.g.f.: exp(x*y/(1-3*x)).
%F A308281 T(n,k) = 3^(n-k)*binomial(n-1, k-1)*n!/k! = 3^(n-k)*A105278.
%e A308281 Triangle begins:
%e A308281      1;
%e A308281      6,    1;
%e A308281     54,   18,    1;
%e A308281    648,  324,   36,  1;
%e A308281   9720, 6480, 1080, 60, 1;
%e A308281   ...
%t A308281 Table[3^(n - k) * Binomial[n - 1, k - 1] * n! / k!, {n, 1, 10}, {k, 1, n}] // Flatten (* _Amiram Eldar_, Jul 13 2019 *)
%Y A308281 Cf. A105278.
%K A308281 nonn,tabl,easy
%O A308281 1,2
%A A308281 _Shuhei Tsujie_, May 18 2019