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A022197
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Gaussian binomial coefficients [ n,6 ] for q = 3.
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1
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1, 1093, 896260, 678468820, 500777836042, 366573514642546, 267598665689058580, 195168545232713290660, 142299528422960399756323, 103741619611085612124067759, 75628919722004322604209288760, 55133793282290501540016988429720
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OFFSET
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6,2
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LINKS
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FORMULA
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G.f.: x^6/((1-x)*(1-3*x)*(1-9*x)*(1-27*x)*(1-81*x)*(1-243*x)*(1-729*x)). - Vincenzo Librandi, Aug 07 2016
a(n) = Product_{i=1..6} (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, 6, 3) for n in range(6, 18)] # Zerinvary Lajos, May 25 2009
(Magma) r:=6; 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=6; 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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