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

Author

Shuhei Tsujie, May 27 2019

Keywords

• nonn
• tabl

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).

Examples

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

Links

• 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.

Crossrefs

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

Formula

E.g.f.: exp((exp(x)-1)*y/(3-2exp(x))).