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Number of flags in an n-dimensional vector space over GF(2).
12

%I #21 Aug 02 2018 16:34:29

%S 1,1,4,36,696,27808,2257888,369572160,121459776768,79991977040128,

%T 105466641591287296,278244130564826548224,1468496684404408240109568,

%U 15502543140842029367582248960,327332729703063815298568073396224,13823536566775628445052117519260598272

%N Number of flags in an n-dimensional vector space over GF(2).

%H Vincenzo Librandi, <a href="/A289545/b289545.txt">Table of n, a(n) for n = 0..80</a>

%H Geoffrey Critzer, <a href="https://esirc.emporia.edu/handle/123456789/3595">Combinatorics of Vector Spaces over Finite Fields</a>, Master's thesis, Emporia State University, 2018.

%H Kent E. Morrison, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL9/Morrison/morrison37.html">Integer Sequences and Matrices Over Finite Fields</a>, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.1.

%F a(n) = Sum A005329(n)/( A005329(n_1)*A005329(n_2)*...*A005329(n_k) ) where the sum is over all compositions of n = n_1 + n_2 + ... + n_k.

%F G.f. a(n)/A005329(n) is the coefficient of x^n in 1/(2 - eq(x)) where eq(x) is the q-exponential function.

%t nn = 15; eq[z_] :=Sum[z^n/FunctionExpand[QFactorial[n, q]], {n, 0, nn}];Table[FunctionExpand[QFactorial[n, q]] /. q -> 2, {n, 0,

%t nn}] CoefficientList[Series[ 1/(1 - (eq[z] - 1)) /. q -> 2, {z, 0, nn}], z]

%K nonn

%O 0,3

%A _Geoffrey Critzer_, Jul 28 2017