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A308282 The fifth power of the unsigned Lah triangular matrix A105278. 0
1, 10, 1, 150, 30, 1, 3000, 900, 60, 1, 75000, 30000, 3000, 100, 1, 2250000, 1125000, 150000, 7500, 150, 1, 78750000, 47250000, 7875000, 525000, 15750, 210, 1, 3150000000, 2205000000, 441000000, 36750000, 1470000, 29400, 280, 1, 141750000000, 113400000000, 26460000000, 2646000000, 132300000, 3528000, 50400, 360, 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, -4 <= d <= 5).

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/(1-5*x)).

T(n,k) = 5^(n-k)*binomial(n-1, k-1)*n!/k! = 5^(n-k)*A105278.

EXAMPLE

Triangle begins:

      1;

     10,     1;

    150,    30,    1;

   3000,   900,   60,   1;

  75000, 30000, 3000, 100, 1;

  ...

MATHEMATICA

Table[5^(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: A192357 A156286 A049223 * A223512 A131367 A048176

Adjacent sequences:  A308279 A308280 A308281 * A308283 A308284 A308285

KEYWORD

nonn,tabl,easy

AUTHOR

Shuhei Tsujie, May 18 2019

STATUS

approved

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Last modified October 27 13:35 EDT 2021. Contains 348276 sequences. (Running on oeis4.)