A308440 Matrix product of triangle of Stirling numbers of second kind A008277 and square of unsigned Lah triangle A105278.

1, 5, 1, 37, 15, 1, 365, 223, 30, 1, 4501, 3675, 745, 50, 1, 66605, 68071, 18450, 1865, 75, 1, 1149877, 1411515, 479101, 64750, 3920, 105, 1, 22687565, 32512663, 13260030, 2244501, 181650, 7322, 140, 1, 503589781, 825175275, 393017185, 79948050, 8103711, 436590, 12558, 180, 1

Offset

1,2

Comments

Also the number of k-dimensional flats of the extended Catalan arrangement of dimension n consisting of hyperplanes x_i - x_j = d (1 <= i < j <= n, -2 <= d <= 2).

Links

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

Robert Gill, The number of elements in a generalized partition semilattice, Discrete mathematics 186.1-3 (1998): 125-134.

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((exp(x)-1)*y/(3-2exp(x))).

Example

Triangle begins:
     1;
     5,    1;
    37,   15,   1;
   365,  223,  30,  1;
  4501, 3675, 745, 50, 1;
  ...

Crossrefs

Cf. A008277, A105278, A050351 (first column), A109092 (row sums).

Sequence in context: A089515 A158820 A082437 * A039817 A293604 A000321

Adjacent sequences: A308437 A308438 A308439 * A308441 A308442 A308443

Keyword

nonn,tabl

Author

Shuhei Tsujie, May 27 2019

Status

approved