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A053601
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Number of bases of an n-dimensional vector space over GF(2).
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13
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1, 1, 3, 28, 840, 83328, 27998208, 32509919232, 132640470466560, 1927943976061501440, 100981078400558897823744, 19242660536873338307044442112, 13448310596010038676027219703234560, 34707333779115158227208335860718444216320, 332718225878012276874300952228513073208156487680
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OFFSET
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0,3
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REFERENCES
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R. Lidl and H. Niederreiter, Introduction to Finite Fields and Their Applications, Cambridge 1986
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LINKS
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FORMULA
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a(n) = (2^n-1)(2^n-2)...(2^n-2^(n-1))/n! = A002884(n)/n!.
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EXAMPLE
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a(2)=3 because the 3 bases are {01,10}, {01,11}, {10,11}.
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MATHEMATICA
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Table[Product[2^n - 2^k, {k, 0, n-1}]/n!, {n, 0, 20}] (* G. C. Greubel, May 16 2019 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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Fred Galvin (galvin(AT)math.ukans.edu), Jan 20 2000
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EXTENSIONS
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STATUS
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approved
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