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
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