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A308281 The third power of the unsigned Lah triangular matrix A105278. 0
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified December 5 12:24 EST 2021. Contains 349557 sequences. (Running on oeis4.)