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A289545
Number of flags in an n-dimensional vector space over GF(2).
12
1, 1, 4, 36, 696, 27808, 2257888, 369572160, 121459776768, 79991977040128, 105466641591287296, 278244130564826548224, 1468496684404408240109568, 15502543140842029367582248960, 327332729703063815298568073396224, 13823536566775628445052117519260598272
OFFSET
0,3
LINKS
Geoffrey Critzer, Combinatorics of Vector Spaces over Finite Fields, Master's thesis, Emporia State University, 2018.
Kent E. Morrison, Integer Sequences and Matrices Over Finite Fields, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.1.
FORMULA
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.
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.
MATHEMATICA
nn = 15; eq[z_] :=Sum[z^n/FunctionExpand[QFactorial[n, q]], {n, 0, nn}]; Table[FunctionExpand[QFactorial[n, q]] /. q -> 2, {n, 0,
nn}] CoefficientList[Series[ 1/(1 - (eq[z] - 1)) /. q -> 2, {z, 0, nn}], z]
CROSSREFS
Sequence in context: A029989 A163887 A156630 * A322782 A145565 A360903
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, Jul 28 2017
STATUS
approved