A308282 The fifth power of the unsigned Lah triangular matrix A105278.

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

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