A145902 Triangular array: rows are the f-vectors of simplicial complexes dual to permutohedra of type D_n.

1, 1, 1, 1, 4, 4, 1, 14, 36, 24, 1, 48, 240, 384, 192, 1, 162, 1440, 4160, 4800, 1920, 1, 536, 8216, 38400, 76800, 69120, 23040, 1, 1738, 45528, 326032, 1008000, 1532160, 1128960, 322560, 1, 5536, 247456, 2634240, 11854080, 27095040, 33116160

Offset: 0

Author

Peter Bala, Oct 29 2008

Keywords

• easy
• nonn
• tabl

Comments

The root systems of type D_n are only defined for n >= 2. It is convenient to add two initial rows to the array to give a lower triangular array. See A066094 for the corresponding array of h-vectors of type D permutohedra.

Examples

			The triangle begins
n\k|..0.....1.....2.....3.....4.....5
=====================================
0..|..1
1..|..1.....1
2..|..1.....4.....4
3..|..1....14....36....24
4..|..1....48...240...384...192
5..|..1...162..1440..4160..4800..1920
...
		

Crossrefs

Cf. A019538 (f-vectors type A permutohedra), A080254 (row sums), A066094 (h-vectors type D permutohedra), A145901 (f-vectors type B permutohedra).

Formula

E.g.f. : ((1 + x)*z - exp(z))/(x*exp(2*z) - (1 + x)) = 1 + x*z + (1 + 4*x + 4*x^2)*z^2/2! + (1 + 14*x + 36*x^2 + 24*x^3)*z^3/3! + ... .

Row sums A080254.

Extensions

Corrected typo. - Peter Bala, Oct 31 2008