A022195 - OEIS

%I #19 Sep 08 2022 08:44:46

%S 1,8191,44731051,209386049731,914807651274739,3867895279362300499,

%T 16094312257426532376339,66441249531569955747981459,

%U 273210326382611632738979052435,1121258922081448861468067825426835,4597164868683271949171164500871212435

%N Gaussian binomial coefficients [ n,12 ] for q = 2.

%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="/A022195/b022195.txt">Table of n, a(n) for n = 12..200</a>

%F a(n) = Product_{i=1..12} (2^(n-i+1)-1)/(2^i-1), by definition. - _Vincenzo Librandi_, Aug 03 2016

%t Table[QBinomial[n, 12, 2], {n, 12, 200}] (* _Vincenzo Librandi_, Aug 03 2016 *)

%o (Sage) [gaussian_binomial(n,12,2) for n in range(12,23)] # _Zerinvary Lajos_, May 25 2009

%o (Magma) r:=12; q:=2; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..25]]; // _Vincenzo Librandi_, Aug 03 2016

%o (PARI) r=12; q=2; for(n=r,30, print1(prod(j=1,r,(1-q^(n-j+1))/(1-q^j)), ", ")) \\ _G. C. Greubel_, May 30 2018

%K nonn

%O 12,2

%A _N. J. A. Sloane_

%E Offset changed by _Vincenzo Librandi_, Aug 03 2016