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%I #19 Sep 08 2022 08:44:46
%S 1,305175781,77610214474995931,19100611156944225555440431,
%T 4670708278954101902438990598678556,
%U 1140674654304411569828223908172341508228556,278502847205686141650283863407927164540769884103556
%N Gaussian binomial coefficients [ n,12 ] for q = 5.
%D F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier-North Holland, 1978, p. 698.
%H Vincenzo Librandi, <a href="/A022219/b022219.txt">Table of n, a(n) for n = 12..130</a>
%F G.f.: x^12/((1-x)*(1-5*x)*(1-25*x)*(1-125*x)*(1-625*x)*(1-3125*x)*(1-15625*x)*(1-78125*x)*(1-390625*x)*(1-1953125*x)*(1-9765625*x)*(1-48828125*x)*(1-244140625*x)). - _Vincenzo Librandi_, Aug 10 2016
%F a(n) = Product_{i=1..12} (5^(n-i+1)-1)/(5^i-1), by definition. - _Vincenzo Librandi_, Aug 10 2016
%t Table[QBinomial[n, 12, 5], {n, 12, 20}] (* _Vincenzo Librandi_, Aug 10 2016 *)
%o (Sage) [gaussian_binomial(n,12,5) for n in range(12,18)] # _Zerinvary Lajos_, May 28 2009
%o (Magma) r:=12; q:=5; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // _Vincenzo Librandi_, Aug 10 2016
%o (PARI) r=12; q=5; for(n=r,30, print1(prod(j=1,r,(1-q^(n-j+1))/(1-q^j)), ", ")) \\ _G. C. Greubel_, Jun 07 2018
%K nonn,easy
%O 12,2
%A _N. J. A. Sloane_
%E Offset changed by _Vincenzo Librandi_, Aug 10 2016
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