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 A022193 #26 Jul 05 2025 05:21:03
%S A022193 1,2047,2794155,3269560515,3571013994483,3774561792168531,
%T A022193 3926442969043883795,4052305562169692070035,4165817792093527797314451,
%U A022193 4274137206973266943778085267,4380990637147598617372537398675
%N A022193 Gaussian binomial coefficients [n, 10] for q = 2.
%D A022193 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier-North Holland, 1978, p. 698.
%H A022193 Vincenzo Librandi, <a href="/A022193/b022193.txt">Table of n, a(n) for n = 10..200</a>
%F A022193 a(n) = Product_{i=1..10} (2^(n-i+1)-1)/(2^i-1), by definition. - _Vincenzo Librandi_, Aug 03 2016
%F A022193 G.f. assuming an offset of 0: exp( Sum_{n >= 1} b(11*n)/b(n)*x^n/n ) = 1 + 2047*x + 2794155*x^2 + ..., where b(n) = A000225(n) = 2^n - 1. - _Peter Bala_, Jul 03 2025
%t A022193 Table[QBinomial[n, 10, 2], {n, 10, 40}] (* _Vincenzo Librandi_, Aug 03 2016 *)
%o A022193 (Sage) [gaussian_binomial(n,10,2) for n in range(10,21)] # _Zerinvary Lajos_, May 25 2009
%o A022193 (Magma) r:=10; q:=2; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // _Vincenzo Librandi_, Aug 03 2016
%o A022193 (PARI) r=10; 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 A022193 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 A022193 nonn
%O A022193 10,2
%A A022193 _N. J. A. Sloane_