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 A022190 #34 Jul 05 2025 05:20:48
%S A022190 1,255,43435,6347715,866251507,114429029715,14877590196755,
%T A022190 1919209135381395,246614610741341843,31627961868755063955,
%U A022190 4052305562169692070035,518946525150879134496915,66441249531569955747981459
%N A022190 Gaussian binomial coefficients [n, 7] for q = 2.
%H A022190 Vincenzo Librandi, <a href="/A022190/b022190.txt">Table of n, a(n) for n = 7..200</a>
%F A022190 G.f.: x^7/((1-x)*(1-2*x)*(1-4*x)*(1-8*x)*(1-16*x)*(1-32*x)*(1-64*x)*(1-128*x)). - _Vincenzo Librandi_, Aug 07 2016
%F A022190 a(n) = Product_{i=1..7} (2^(n-i+1)-1)/(2^i-1), by definition. - _Vincenzo Librandi_, Aug 02 2016
%F A022190 G.f. with an offset of 0: exp( Sum_{n >= 1} b(8*n)/b(n)*x^n/n ) = 1 + 255*x + 43435*x^2 + ..., where b(n) = A000225(n) = 2^n - 1. - _Peter Bala_, Jul 01 2025
%t A022190 Table[QBinomial[n, 7, 2], {n, 7, 24}] (* _Vincenzo Librandi_, Aug 02 2016 *)
%o A022190 (Sage) [gaussian_binomial(n,7,2) for n in range(7,20)] # _Zerinvary Lajos_, May 25 2009
%o A022190 (Magma) r:=7; q:=2; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // _Vincenzo Librandi_, Aug 02 2016
%o A022190 (PARI) r=7; 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 A022190 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 A022190 nonn,easy
%O A022190 7,2
%A A022190 _N. J. A. Sloane_, Jun 14 1998
%E A022190 Changed offset by _Vincenzo Librandi_, Aug 02 2016