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 A053601 Number of bases of an n-dimensional vector space over GF(2). 11
 1, 1, 3, 28, 840, 83328, 27998208, 32509919232, 132640470466560, 1927943976061501440, 100981078400558897823744, 19242660536873338307044442112, 13448310596010038676027219703234560 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 REFERENCES R. Lidl and H. Niederreiter, Introduction to Finite Fields and Their Applications, Cambridge 1986 LINKS G. C. Greubel, Table of n, a(n) for n = 0..59 Claude Carlet, Philippe Gaborit, Jon-Lark Kim and Patrick Sole, A new class of codes for Boolean masking of cryptographic computations, arXiv:1110.1193 [cs.IT], 2011-2012. David Ellerman, The number of direct-sum decompositions of a finite vector space, arXiv:1603.07619 [math.CO], 2016. David Ellerman, The Quantum Logic of Direct-Sum Decompositions, arXiv:1604.01087 [quant-ph], 2016. FORMULA a(n) = (2^n-1)(2^n-2)...(2^n-2^(n-1))/n! = A002884(n)/n!. EXAMPLE a(2)=3 because the 3 bases are {01,10}, {01,11}, {10,11}. MATHEMATICA Table[Product[2^n - 2^k, {k, 0, n-1}]/n!, {n, 0, 20}] (* G. C. Greubel, May 16 2019 *) PROG (PARI) a(n) = prod(k=0, n-1, 2^n - 2^k)/n!; \\ Michel Marcus, Mar 25 2016 (MAGMA) [1] cat [(&*[2^n -2^k: k in [0..n-1]])/Factorial(n): n in [1..20]]; // G. C. Greubel, May 16 2019 (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 CROSSREFS Cf. A002884. Sequence in context: A276745 A015474 A324462 * A140990 A196735 A208438 Adjacent sequences:  A053598 A053599 A053600 * A053602 A053603 A053604 KEYWORD easy,nonn AUTHOR Fred Galvin (galvin(AT)math.ukans.edu), Jan 20 2000 EXTENSIONS More terms from Vladeta Jovovic, Apr 05 2000 STATUS approved

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Last modified August 20 01:14 EDT 2019. Contains 326136 sequences. (Running on oeis4.)