%I #27 Apr 30 2024 03:13:02
%S 1,1,3,28,840,83328,27998208,32509919232,132640470466560,
%T 1927943976061501440,100981078400558897823744,
%U 19242660536873338307044442112,13448310596010038676027219703234560,34707333779115158227208335860718444216320,332718225878012276874300952228513073208156487680
%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