This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A022194 #28 Jul 05 2025 05:21:08
%S A022194 1,4095,11180715,26167664835,57162391576563,120843139740969555,
%T A022194 251413193158549532435,518946525150879134496915,
%U A022194 1066968301301093995246996371,2189425218271613769209626653075,4488323837657412597958687922896275
%N A022194 Gaussian binomial coefficients [n, 11] for q = 2.
%D A022194 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier-North Holland, 1978, p. 698.
%H A022194 Vincenzo Librandi, <a href="/A022194/b022194.txt">Table of n, a(n) for n = 11..200</a>
%F A022194 a(n) = Product_{i=1..11} (2^(n-i+1)-1)/(2^i-1), by definition. - _Vincenzo Librandi_, Aug 03 2016
%F A022194 G.f. assuming an offset of 0: exp( Sum_{n >= 1} b(12*n)/b(n)*x^n/n ) = 1 + 4095*x + 11180715*x^2 + ..., where b(n) = A000225(n) = 2^n - 1. - _Peter Bala_, Jul 03 2025
%t A022194 QBinomial[Range[11,30],11,2] (* _Harvey P. Dale_, Oct 21 2014 *)
%o A022194 (Sage) [gaussian_binomial(n,11,2) for n in range(11,22)] # _Zerinvary Lajos_, May 25 2009
%o A022194 (Magma) r:=11; q:=2; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // _Vincenzo Librandi_, Aug 03 2016
%o A022194 (PARI) r=11; 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
%Y A022194 Gaussian binomial coefficient [n, k] for q = 2: A000225 (k = 1), A006095 (k = 2), A006096 (k = 3), A006097 (k = 4), A006110 (k = 5), A022189 - A022195 (k = 6 thru 12).
%K A022194 nonn
%O A022194 11,2
%A A022194 _N. J. A. Sloane_