%I #28 May 22 2022 09:47:52

%S 1,435356467,162458788655384143,59213707780769522731688119,

%T 21499147706200521642647791579711015,

%U 7800830687562794744818371174867996113478343

%N Gaussian binomial coefficients [ n,11 ] for q = 6.

%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="/A022229/b022229.txt">Table of n, a(n) for n = 11..130</a>

%H <a href="https://oeis.org/index/Ga#Gaussian_binomial_coefficients">Index entries for Gaussian binomial coefficients</a>

%F a(n) ~ k*362797056^n for a constant k. - _Charles R Greathouse IV_, Oct 14 2014

%F G.f.: x^11/((1-x)*(1-6*x)*(1-36*x)*(1-216*x)*(1-1296*x)*(1-7776*x)*(1-46656*x)*(1-279936*x)*(1-1679616*x)*(1-10077696*x)*(1-60466176*x)*(1-362797056*x)). - _Vincenzo Librandi_, Aug 12 2016

%F a(n) = Product_{i=1..11} (6^(n-i+1)-1)/(6^i-1), by definition. - _Vincenzo Librandi_, Aug 12 2016

%p seq(eval(expand(QDifferenceEquations:-QBinomial(n,11,q)),q=6),n=11..20); # _Robert Israel_, Oct 14 2014

%t QBinomial[Range[11,20],11,6] (* _Harvey P. Dale_, Oct 06 2014 *)

%o (Sage) [gaussian_binomial(n,11,6) for n in range(11,17)] # _Zerinvary Lajos_, May 28 2009

%o (Magma) r:=11; q:=6; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // _Vincenzo Librandi_, Oct 14 2014

%o (PARI) a(n)=prod(i=1,11,(6^(n-i+1)-1)/(6^i-1)) \\ _Charles R Greathouse IV_, Oct 14 2014

%K nonn,easy

%O 11,2

%A _N. J. A. Sloane_