A022211 - OEIS

%I #17 Sep 08 2022 08:44:46

%S 1,22369621,400319959420837,6822861635108183247077,

%T 114917519925881846404167134693,1929880702992615813429218299211809253,

%U 32385932129579122653905315624401024370889189

%N Gaussian binomial coefficients [ n,12 ] for q = 4.

%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="/A022211/b022211.txt">Table of n, a(n) for n = 12..150</a>

%F G.f.: x^12/((1-x)*(1-4*x)*(1-16*x)*(1-64*x)*(1-256*x)*(1-1024*x)*(1-4096*x)*(1-16384*x)*(1-65636*x)*(1-262144*x)*(1-1048576*x)*(1-4194304*x)*(1-16777216*x)). - _Vincenzo Librandi_, Aug 10 2016

%F a(n) = Product_{i=1..12} (4^(n-i+1)-1)/(4^i-1), by definition. - _Vincenzo Librandi_, Aug 10 2016

%t Table[QBinomial[n, 12, 4], {n, 12, 20}] (* _Vincenzo Librandi_, Aug 10 2016 *)

%o (Sage) [gaussian_binomial(n,12,4) for n in range(12,19)] # _Zerinvary Lajos_, May 28 2009

%o (Magma) r:=12; q:=4; [&*[(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=4; for(n=r,30, print1(prod(j=1,r,(1-q^(n-j+1))/(1-q^j)), ", ")) \\ _G. C. Greubel_, Jun 04 2018

%K nonn,easy

%O 12,2

%A _N. J. A. Sloane_

%E Offset changed by _Vincenzo Librandi_, Aug 10 2016