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A145902 Triangular array: rows are the f-vectors of simplicial complexes dual to permutohedra of type D_n. 2
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

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.

LINKS

Table of n, a(n) for n=0..42.

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.

EXAMPLE

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

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

Sequence in context: A096078 A140313 A102323 * A124028 A123966 A079507

Adjacent sequences:  A145899 A145900 A145901 * A145903 A145904 A145905

KEYWORD

easy,nonn,tabl

AUTHOR

Peter Bala, Oct 29 2008

EXTENSIONS

Corrected typo. - Peter Bala, Oct 31 2008

STATUS

approved

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Last modified October 18 07:00 EDT 2018. Contains 316307 sequences. (Running on oeis4.)