A088729 Matrix product of Stirling2-triangle A008277(n,k) and unsigned Lah-triangle |A008297(n,k)|.

1, 3, 1, 13, 9, 1, 75, 79, 18, 1, 541, 765, 265, 30, 1, 4683, 8311, 3870, 665, 45, 1, 47293, 100989, 59101, 13650, 1400, 63, 1, 545835, 1362439, 960498, 278901, 38430, 2618, 84, 1, 7087261, 20246445, 16700545, 5844510, 1012431, 92610, 4494, 108, 1

Offset: 1

Author

Vladeta Jovovic, Nov 22 2003

Keywords

• nonn
• tabl

Comments

Also the Bell transform of A000670(n+1). For the definition of the Bell transform see A264428. - Peter Luschny, Jan 26 2016

Also the number of k-dimensional flats of the n-dimensional Catalan arrangement. - Shuhei Tsujie, May 05 2019

Links

• 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. A000670(first column), A075729(row sums).

Programs

Maple

# The function BellMatrix is defined in A264428.
# Adds (1, 0, 0, 0, ..) as column 0.
BellMatrix(n -> add(combinat:-eulerian1(n+1, k)*2^k, k=0..n+1), 9); # Peter Luschny, Jan 26 2016

Mathematica

BellMatrix[f_, len_] := With[{t = Array[f, len, 0]}, Table[BellY[n, k, t], {n, 0, len - 1}, {k, 0, len - 1}]];
rows = 12;
B = BellMatrix[Function[n, HurwitzLerchPhi[1/2, -n-1, 0]/2], rows];
Table[B[[n, k]], {n, 2, rows}, {k, 2, n}] // Flatten (* Jean-François Alcover, Jun 27 2018, after Peter Luschny *)

Formula

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