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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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..80 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 Adjacent sequences: A289542 A289543 A289544 * A289546 A289547 A289548 KEYWORD nonn AUTHOR Geoffrey Critzer, Jul 28 2017 STATUS approved

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Last modified December 11 07:17 EST 2023. Contains 367717 sequences. (Running on oeis4.)