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A053601 Number of bases of an n-dimensional vector space over GF(2). 11


%S 1,1,3,28,840,83328,27998208,32509919232,132640470466560,

%T 1927943976061501440,100981078400558897823744,

%U 19242660536873338307044442112,13448310596010038676027219703234560

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

%D R. Lidl and H. Niederreiter, Introduction to Finite Fields and Their Applications, Cambridge 1986

%H G. C. Greubel, <a href="/A053601/b053601.txt">Table of n, a(n) for n = 0..59</a>

%H Claude Carlet, Philippe Gaborit, Jon-Lark Kim and Patrick Sole, <a href="http://arxiv.org/abs/1110.1193">A new class of codes for Boolean masking of cryptographic computations</a>, arXiv:1110.1193 [cs.IT], 2011-2012.

%H David Ellerman, <a href="http://arxiv.org/abs/1603.07619">The number of direct-sum decompositions of a finite vector space</a>, arXiv:1603.07619 [math.CO], 2016.

%H David Ellerman, <a href="http://arxiv.org/abs/1604.01087">The Quantum Logic of Direct-Sum Decompositions</a>, arXiv:1604.01087 [quant-ph], 2016.

%F a(n) = (2^n-1)(2^n-2)...(2^n-2^(n-1))/n! = A002884(n)/n!.

%e a(2)=3 because the 3 bases are {01,10}, {01,11}, {10,11}.

%t Table[Product[2^n - 2^k, {k,0,n-1}]/n!, {n,0,20}] (* _G. C. Greubel_, May 16 2019 *)

%o (PARI) a(n) = prod(k=0, n-1, 2^n - 2^k)/n!; \\ _Michel Marcus_, Mar 25 2016

%o (MAGMA) [1] cat [(&*[2^n -2^k: k in [0..n-1]])/Factorial(n): n in [1..20]]; // _G. C. Greubel_, May 16 2019

%o (Sage) [product(2^n -2^k for k in (0..n-1))/factorial(n) for n in (0..20)] # _G. C. Greubel_, May 16 2019

%Y Cf. A002884.

%K easy,nonn

%O 0,3

%A Fred Galvin (galvin(AT)math.ukans.edu), Jan 20 2000

%E More terms from _Vladeta Jovovic_, Apr 05 2000

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Last modified July 27 21:21 EDT 2021. Contains 346316 sequences. (Running on oeis4.)