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A022207
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Gaussian binomial coefficients [ n,8 ] for q = 4.
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1
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1, 87381, 6108368805, 406672215935205, 26756185103024942565, 1755207390500040817377765, 115057361291389776393497498085, 7540859480106603961931048583270885, 494205307747746503853075131001823990245
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OFFSET
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8,2
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REFERENCES
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F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier-North Holland, 1978, p. 698.
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LINKS
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FORMULA
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G.f.: x^8/((1-x)*(1-4*x)*(1-16*x)*(1-64*x)*(1-256*x)*(1-1024*x)*(1-4096*x)*(1-16384*x)*(1-65536*x)). - Vincenzo Librandi, Aug 11 2016
a(n) = Product_{i=1..8} (4^(n-i+1)-1)/(4^i-1), by definition. - Vincenzo Librandi, Aug 11 2016
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MATHEMATICA
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PROG
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(Sage) [gaussian_binomial(n, 8, 4) for n in range(8, 17)] # Zerinvary Lajos, May 25 2009
(Magma) r:=8; q:=4; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Aug 11 2016
(PARI) r=8; q=4; for(n=r, 30, print1(prod(j=1, r, (1-q^(n-j+1))/(1-q^j)), ", ")) \\ G. C. Greubel, Jun 04 2018
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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