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A022199
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Gaussian binomial coefficients [ n,8 ] for q = 3.
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1
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1, 9841, 72636421, 494894285941, 3287582741506063, 21658948312410865183, 142299528422960399756323, 934054234760012359481199283, 6129263888495201102915629695046, 40216143252770054194345243936096486, 263862583736385343242102717216527933566
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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)*(1-3*x)*(1-9*x)*(1-27*x)*(1-81*x)*(1-243*x)*(1-729*x)*(1-2187*x)*(1-6561*x)). - Vincenzo Librandi, Aug 07 2016
a(n) = Product_{i=1..8} (3^(n-i+1)-1)/(3^i-1), by definition. - Vincenzo Librandi, Aug 07 2016
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MATHEMATICA
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PROG
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(Sage) [gaussian_binomial(n, 8, 3) for n in range(8, 19)] # Zerinvary Lajos, May 25 2009
(Magma) r:=8; q:=3; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Aug 07 2016
(PARI) r=8; q=3; for(n=r, 30, print1(prod(j=1, r, (1-q^(n-j+1))/(1-q^j)), ", ")) \\ G. C. Greubel, May 30 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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