A308281 - OEIS

A308281

The third power of the unsigned Lah triangular matrix A105278.

1, 6, 1, 54, 18, 1, 648, 324, 36, 1, 9720, 6480, 1080, 60, 1, 174960, 145800, 32400, 2700, 90, 1, 3674160, 3674160, 1020600, 113400, 5670, 126, 1, 88179840, 102876480, 34292160, 4762800, 317520, 10584, 168, 1, 2380855680, 3174474240, 1234517760, 205752960, 17146080, 762048, 18144, 216, 1

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OFFSET

1,2

COMMENTS

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).

LINKS

Table of n, a(n) for n=1..45.

N. Nakashima and S. Tsujie, Enumeration of Flats of the Extended Catalan and Shi Arrangements with Species, arXiv:1904.09748 [math.CO], 2019.

FORMULA

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

T(n,k) = 3^(n-k)*binomial(n-1, k-1)*n!/k! = 3^(n-k)*A105278.

EXAMPLE

Triangle begins:

6, 1;

54, 18, 1;

648, 324, 36, 1;

9720, 6480, 1080, 60, 1;