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

%I A145902 #5 Sep 16 2020 05:03:07
%S A145902 1,1,1,1,4,4,1,14,36,24,1,48,240,384,192,1,162,1440,4160,4800,1920,1,
%T A145902 536,8216,38400,76800,69120,23040,1,1738,45528,326032,1008000,1532160,
%U A145902 1128960,322560,1,5536,247456,2634240,11854080,27095040,33116160
%N A145902 Triangular array: rows are the f-vectors of simplicial complexes dual to permutohedra of type D_n.
%C A145902 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.
%F A145902 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! + ... .
%F A145902 Row sums A080254.
%e A145902 The triangle begins
%e A145902 n\k|..0.....1.....2.....3.....4.....5
%e A145902 =====================================
%e A145902 0..|..1
%e A145902 1..|..1.....1
%e A145902 2..|..1.....4.....4
%e A145902 3..|..1....14....36....24
%e A145902 4..|..1....48...240...384...192
%e A145902 5..|..1...162..1440..4160..4800..1920
%e A145902 ...
%Y A145902 Cf. A019538 (f-vectors type A permutohedra), A080254 (row sums), A066094 (h-vectors type D permutohedra), A145901 (f-vectors type B permutohedra).
%K A145902 easy,nonn,tabl
%O A145902 0,5
%A A145902 _Peter Bala_, Oct 29 2008
%E A145902 Corrected typo. - _Peter Bala_, Oct 31 2008