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Search: id:A145902
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| A145902 |
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Triangular array: rows are the f-vectors of simplicial complexes dual to permutohedra of type D_n. |
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+0
3
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| 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; listen)
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OFFSET
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0,5
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COMMENT
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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.
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FORMULA
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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.
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EXAMPLE
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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
...
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CROSSREFS
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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 this_sequence A124028 A123966 A079507
Adjacent sequences: A145899 A145900 A145901 this_sequence A145903 A145904 A145905
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Peter Bala (pbala(AT)toucansurf.com), Oct 29 2008
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EXTENSIONS
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Corrected typo. - Peter Bala (pbala(AT)toucansurf.com), Oct 31 2008
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