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

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:
     1;
     6,    1;
    54,   18,    1;
   648,  324,   36,  1;
  9720, 6480, 1080, 60, 1;
  ...

Mathematica

Table[3^(n - k) * Binomial[n - 1, k - 1] * n! / k!, {n, 1, 10}, {k, 1, n}] // Flatten (* Amiram Eldar, Jul 13 2019 *)

Crossrefs

Cf. A105278.

Sequence in context: A290316 A090435 A136237 * A347211 A083837 A049213

Adjacent sequences: A308278 A308279 A308280 * A308282 A308283 A308284

Keyword

nonn,tabl,easy

Author

Shuhei Tsujie, May 18 2019

Status

approved