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A053601
Number of bases of an n-dimensional vector space over GF(2).
14
1, 1, 3, 28, 840, 83328, 27998208, 32509919232, 132640470466560, 1927943976061501440, 100981078400558897823744, 19242660536873338307044442112, 13448310596010038676027219703234560, 34707333779115158227208335860718444216320, 332718225878012276874300952228513073208156487680
OFFSET
0,3
REFERENCES
R. Lidl and H. Niederreiter, Introduction to Finite Fields and Their Applications, Cambridge 1986
LINKS
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: A354664 A015474 A324462 * A328791 A140990 A196735
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